% Time-stamp: <2000-05-14 15:54:30 whitcher>
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% BIBLIOGRAPHY OF WAVELET, TIME-SERIES, AND RELATED DOCUMENTS
%
% Brandon J Whitcher
% EURANDOM, P.O. Box 513
% 5600 MB Eindhoven, The Netherlands
% whitcher@eurandom.tue.nl
% http://www.eurandom.tue.nl/whitcher
%
%
% Please don't remove this header if you copy or transfer this file.
%
%
@String{AandA = "Astronomy and Astrophysics"}
@String{AAP = "Annals of Applied Probability"}
@String{AASS = "Astronomy \& Astrophysics Supplement Series"}
@String{ACHA = "Applied and Computational Harmonic Analysis"}
@String{AG = "Annales Geophysicae"}
@String{AML = "Applied Mathematical Letters"}
@String{AMM = "American Mathematical Monthly"}
@String{AMS = "American Mathematical Society"}
@String{AnJ = "The Astronomical Journal"}
@String{AofMS = "The Annals of Mathematical Statistics"}
@String{AofS = "Annals of Statistics"}
@String{ApJ = "The Astrophysical Journal"}
@String{AS = "Applied Statistics"}
@String{BAMathS = "Bulletin of the American Mathematical Society
(N.S.)"}
@String{BAMetS = "Bulletin of the American Meteorological Society"}
@String{Ber = "Bernoulli"}
@String{BKA = "Biometrika"}
@String{BLM = "Boundary-Layer Meteorology"}
@String{CE = "Computational Economics"}
@String{CG = "Chemical Geology"}
@String{CS = "Computational Statistics"}
@String{CSA = "Communications in Statistics A"}
@String{CSB = "Communications in Statistics B"}
@String{CSDA = "Computational Statistics \& Data Analysis"}
@String{CSS = "Computing Science and Statistics"}
@String{ECA = "Econometrica"}
@String{ECJ3 = "Electronics and Communications in Japan 3"}
@String{EE = "Empirical Economics"}
@String{EI = "Earth Interactions"}
@String{EL = "Economics Letters"}
@String{EP = "Environmental Pollution"}
@String{ET = "Econometric Theory"}
@String{FS = "Financial Stochastics"}
@String{GJI = "Geophysical Journal International"}
@String{GJRAS = "Geophysical Journal of the Royal Astronomical
Society"}
@String{GP = "Geophysical Prospecting"}
@String{GRL = "Geophysical Research Letters"}
@String{IEICETFECCS = "IEICE Transactions on Fundamentals of
Electronics Communications and Computer Science"}
@String{IEEEAPM = "IEEE Antennas and Propagation Magazine"}
@String{IEEECSE = "IEEE Computational Science and Engineering"}
@String{IEEEP = "IEEE Proceedings"}
@String{IEEES = "IEEE Spectrum"}
@String{IEEESPL = "IEEE Signal Processing Letters"}
@String{IEEESPM = "IEEE Signal Processing Magazine"}
@String{IEEESPS = "IEEE Signal Processing Society"}
@String{IEEETAC = "IEEE Transactions on Automatic Control"}
@String{IEEETAE = "IEEE Transactions on Audio and Electroacoustics"}
@String{IEEETAES = "IEEE Transactions on Aerospace and Electronic
Systems"}
@String{IEEETASSP = "IEEE Transactions on Acoustics, Speech, and Signal
Processing"}
@String{IEEETC = "IEEE Transactions on Communications"}
@String{IEEETCS = "IEEE Transactions on Circuits and Systems"}
@String{IEEETCS2 = "IEEE Transactions on Circuits and Systems--II"}
@String{IEEETGRS = "IEEE Transactions on Geoscience and Remote Sensing"}
@String{IEEETIM = "IEEE Transactions on Instrumentation and
Measurement"}
@String{IEEETIP = "IEEE Transactions on Image Processing"}
@String{IEEETIT = "IEEE Transactions on Information Theory"}
@String{IEEETMI = "IEEE Transactions on Medical Imaging"}
@String{IEEETPAMI = "IEEE Transactions on Pattern Analysis and Machine
Intelligence"}
@String{IEEETSP = "IEEE Transactions on Signal Processing"}
@String{IJC = "International Journal of Climatology"}
@String{IJE = "International Journal of Electronics"}
@String{IJF = "International Journal of Forecasting"}
@String{JAcSA = "Journal of the Acoustical Society of America"}
@String{JAM = "Journal of Applied Meteorology"}
@String{JAOT = "Journal of Atmospheric and Oceanic Technology"}
@String{JAS = "Journal of Atmospheric Science"}
@String{JASA = "Journal of the American Statistical Association"}
@String{JASS = "Journal of Applied Statistical Science"}
@String{JAT = "Journal of Approximation Theory"}
@String{JBES = "Journal of Business and Economic Statistics"}
@String{JC = "Journal of Climate"}
@String{JCGS = "Journal of Computational and Graphical Statistics"}
@String{JCty = "Journal of Climatology"}
@String{JEcol = "Journal of Ecology"}
@String{JEcon = "Journal of Econometrics"}
@String{JEDC = "Journal of Economic Dynamics and Control"}
@String{JETE = "Journal of Economic Theory and Econometrics"}
@String{JF = "Journal of Forecasting"}
@String{JFAA = "Journal of Fourier Analysis and Applications"}
@String{JFM = "Journal of Fluid Mechanics"}
@String{JGR = "Journal of Geophysical Research"}
@String{JGRA = "Journal of Geophysical Research -- Atmospheres"}
@String{JISS = "Journal of the Italian Statistical Society"}
@String{JMP = "Journal of Mathematical Physics"}
@String{JMS = "Journal of the Meteorological Society"}
@String{JNS = "Journal of Nonparametric Statistics"}
@String{JPA = "Journal of Physics A"}
@String{JPO = "Journal of Physical Oceanography"}
@String{JRSSA = "Journal of the Royal Statistical Society A"}
@String{JRSSB = "Journal of the Royal Statistical Society B"}
@String{JSCS = "Journal of Statistical Computation and Simulation"}
@String{JTSA = "Journal of Time Series Analysis"}
@String{JVA = "Journal of Vibration and Acoustics"}
@String{JVCIR = "Journal of Visual Communication and Image
Representation"}
@String{KKA = "Kybernetika"}
@String{MCM = "Mathematical and Computer Modelling"}
@String{MKA = "Metrika"}
@String{MWR = "Monthly Weather Review"}
@String{NJ = "New Jersey"}
@String{NY = "New York"}
@String{OE = "Optical Engineering"}
@String{PEM = "Probability Engineering Mechanics"}
@String{PIEEE = "Proceedings of the IEEE"}
@String{PR = "Pattern Recognition"}
@String{PRE = "Physical Review E"}
@String{PRL = "Physical Review Letters"}
@String{PRSLA = "Proceedings of the Royal Society of London, Series A"}
@String{PTRSLA = "Philosophical Transactions of the Royal Society of
London A"}
@String{QJRMS = "Quarterly Journal of the Royal Meteorological
Society"}
@String{RES = "Review of Economic Studies"}
@String{SC = "Statistics and Computing"}
@String{SD = "San Diego"}
@String{SF = "San Francisco"}
@String{SIAM = "Society for Industrial and Applied Mathematics"}
@String{SIAMJMA = "SIAM Journal of Mathematical Analysis"}
@String{SIAMJSC = "SIAM Journal of Scientific Computing"}
@String{SIAMJSSC = "SIAM Journal on Scientific and Statistical
Computing"}
@String{SiG = "Surveys in Geophysics"}
@String{SINUM = "SIAM Journal of Numerical Analysis"}
@String{SIREV = "SIAM Review"}
@String{SJS = "Scandanavian Journal of Statistics"}
@String{SN = "Statistica Neerlandica"}
@String{SNDE = "Studies in Nonlinear Dynamics and Economics"}
@String{SP = "Signal Processing"}
@String{SPIE = "The International Society for Optical Engineering"}
@String{SPL = "Statistics \& Probability Letters"}
@String{SPTA = "Stochastic Processes and Their Applications"}
@String{SS = "Statistical Science"}
@String{SSin = "Statistica Sinica"}
@String{TAS = "The American Statistician"}
@String{TECH = "Technometrics"}
@String{TIEICEA = "Transactions of the Institute of Electronics,
Information and Communication Engineers A"}
@String{TPIA = "Theory of Probability and Its Applications"}
@String{WRR = "Water Resources Research"}
%%%%%----------%%%%%----------%%%%%----------%%%%%----------%%%%%
@Article{abr-ben:adaptive,
title = "Adaptive thresholding of wavelet coefficients",
author = "Felix Abramovich and Y. Benjamini",
journal = CSDA,
volume = "22",
pages = "351--361",
year = "1996",
URL = "http://www.math.tau.ac.il/~felix/ltx/JCSDA.ps.gz",
email = "felix@math.tau.ac.il",
}
@InCollection{abr-ben:thresholding,
title = "Thresholding of wavelet coefficients as multiple
hypotheses testing procedure",
author = "Felix Abramovich and Y. Benjamini",
pages = "5--14",
crossref = "ant-opp:wavelets",
URL = "http://www.math.tau.ac.il/~felix/Papers.html",
email = "felix@math.tau.ac.il",
abstract = "",
}
@Unpublished{abr-etal:scaling,
title = "Wavelets for the analysis, estimation and synthesis
of scaling data",
author = "P. Abry and P. Flandrin and M. S. Taqqu and
D. Veitch",
year = "1998",
note = "preprint",
URL = "http://www.serc.rmit.edu.au/~darryl/wwbook.ps",
}
@Article{abr-fla:initial,
title = "{O}n the initialization of the discrete wavelet
transform algorithm",
author = "P. Abry and P. Flandrin",
journal = IEEESPL,
volume = "1",
number = "2",
year = "1994",
pages = "32--34",
abstract = "The authors show that making use of the discrete
wavelet transform to analyse data implies performing
a preliminary initialization of the fast pyramidal
algorithm. An approximation enabling easy
performance of such an initialization is proposed.",
keywords = "initialization. discrete wavelet transform
algorithm. fast pyramidal algorithm. performance.",
}
@InProceedings{abr-gon-fla:based,
title = "Wavelet-based spectral analysis of $1/f$ processes",
author = "P. Abry and P. Gon\c{c}alv{\`e}s and P. Flandrin",
booktitle = "Proceedings of the IEEE International Conference on
Acoustics, Speech, and Signal Processing",
volume = "3",
year = "1993",
pages = "237--240",
note = "Minneapolis, MN, USA",
keywords = "1/f processes, time-scale-based spectral estimation,
matched tilings, time-frequency plane, probability
density function, discrete wavelet scheme, minimum
variance estimator, weighted least-squares",
abstract = "The authors attempt to show how and why a
time-scale-based spectral estimation naturally suits
the nature of $1/f$ processes, characterized by a
power spectral density proportional to
$|\nu|^{-\alpha}$. They show that a time-scale
approach allows an unbiased estimation of the
spectral exponent alpha and interpret this result in
terms of matched tilings of the time-frequency
plane. They derive explicitly the probability
density function of the estimated value of
$\alpha$. From this analysis, they find that there
exists an optimum number of scales to use in a
discrete wavelet scheme for obtaining a minimum
variance estimator and that an improved procedure
can be designed by making use of weighted
least-squares in the estimation.",
}
@InProceedings{abr-gon-fla:spectrum,
title = "Wavelets, spectrum analysis and 1/f processes",
author = "P. Abry and P. Gon\c{c}alv{\`e}s and P. Flandrin",
pages = "15--29",
crossref = "ant-opp:wavelets",
keywords = "",
abstract = "The purpose of this paper is to evidence why
wavelet-based estimators are naturally matched to
the spectrum analysis of $1/f$ processes. It is
shown how the revisiting of classical spectral
estimators from a time-frequency perspective allows
to define different wavelet-based generalizations
which are proved to be statistically and
computationally efficient. Discretization issues (in
time and scale) are discussed in some detail,
theoretical claims are supported by numerical
experiments and the importance of the proposed
approach in turbulence studies is underlined.",
}
@Unpublished{abr-sap-sil:bayesian,
title = "Wavelet thresholding via a {B}ayesian approach",
author = "Felix Abramovich and T. Sapatinas and Bernard
Silverman",
year = "1996",
note = "Submitted",
URL = "http://www.math.tau.ac.il/~felix/ltx/Bayes.ps.gz",
email = "felix@math.tau.ac.il",
}
@Article{abr-sel:synthesis,
title = "The wavelet-based synthesis for fractional {B}rownian
motion - {P}roposed by {F}. {S}ellan and {Y}. {M}eyer:
{R}emarks and fast implementation",
author = "P. Abry and F. Sellan",
journal = ACHA,
volume = "3",
number = "4",
pages = "377--383",
year = "1996",
}
@Article{abr-sil:inverse,
title = "Wavelet decomposition approaches to statistical
inverse problems",
author = "F. Abramovich and B. W. Silverman",
journal = BKA,
volume = "85",
number = "1",
pages = "115--129",
year = "1998",
keywords = "exact risk analysis. near-minimax estimation. singular
value decomposition. spatially adaptive estimation.
statistical linear inverse problem. vaguelette.
wavelet.",
abstract = "A wide variety of scientific settings involve indirect
noisy measurements where one faces a linear inverse
problem in the presence of noise. Primary interest is
in some function f(t) but data are accessible only
about some linear transform corrupted by noise; The
usual linear methods for such inverse problems do not
perform satisfactorily when f(t) is spatially
inhomogeneous. One existing nonlinear alternative is
the wavelet-vaguelette decomposition method, based on
the expansion of the unknown f(t) in wavelet series. In
the vaguelette- wavelet decomposition method proposed
here, the observed data are expanded directly in
wavelet series. The performances of various methods are
compared through exact risk calculations, in the
context of the estimation of the derivative of a
function observed subject to noise. A result is proved
demonstrating that, with a suitable universal threshold
somewhat larger than that used for standard denoising
problems, both the wavelet-based approaches have an
ideal spatial adaptivity property.",
}
@Article{abr-vei-fla:revisiting,
title = "Long Range Dependence: {R}evisiting Aggregation with
Wavelets",
author = "Patrice Abry and Darryl Veitch and Patrick Flandrin",
journal = JTSA,
volume = "19",
number = "3",
pages = "253--266",
year = "1998",
URL = "http://www.serc.rmit.edu.au/~darryl/A2.ps",
keywords = "long-range dependence, self-similarity, aggregation,
multiresolution analysis, wavelet transform, parameter
estimation",
abstract = "The aggregation procedure is a natural way to analyse
signals which exhibit long-range dependent features and
has been used as a basis for estimation of the Hurst
parameter, H. In this paper it is shown how aggregation
can be naturally rephrased within the wavelet transform
framework, being directly related to approximations of
the signal in the sense of a Haar-multiresolution
analysis. A natural wavelet based generalisation to
traditional aggregation is then proposed:
``a-aggregation''. It is shown that a-aggregation
cannot lead to good estimators of H, and so a new kind
of aggregation, ``d-aggregation'', is defined, which is
related to the details rather than the approximations
of a multiresolution analysis. An estimator of H based
on d-aggregation has excellent statistical and
computational properties, whilst preserving the spirit
of aggregation. The estimator is applied to
telecommunications network data.",
}
@Article{abr-vei:traffic,
title = "Wavelet analysis of long-range-dependent traffic",
author = "P. Abry and D. Veitch",
journal = IEEETIT,
volume = "44",
number = "1",
pages = "2--15",
year = "1998",
URL = "http://www.serc.rmit.edu.au/~darryl/A1.ps",
keywords = "Hurst parameter long-range dependence packet traffic
parameter estimation stationarity telecommunications
networks time-scale analysis wavelet decomposition",
abstract = "A wavelet-based tool for the analysis of long-range
dependence and a related semi-parametric estimator of
the Hurst parameter is introduced, The estimator is
shown to be unbiased under very general conditions, and
efficient under Gaussian assumptions. It can be
implemented very efficiently allowing the direct
analysis of very large data sets, and is highly robust
against the presence of deterministic trends, as wed as
allowing their detection and identification.
Statistical, computational, and numerical comparisons
are made against traditional estimators including that
of Whittle. The estimator is used to perform a thorough
analysis of the long-range dependence in Ethernet
traffic traces, New features are found with important
implications for the choice of valid models for
performance evaluation, A study of mono versus
multifractality is also performed, and a preliminary
study of the stationarity with respect to the Hurst
parameter and deterministic trends.",
}
@Book{ack:real-time,
title = "Real-Time Signal Processing: Design and
Implementation of Signal Processing Systems",
booktitle = "Real-Time Signal Processing: Design and
Implementation of Signal Processing Systems",
author = "John G. Ackenhusen",
publisher = "Prentice Hall",
address = "Upper Saddle River, NJ",
year = "1999",
pages = "461",
}
@TechReport{agu:evaluating,
title = "Wavelet and Autoregressive Decompositions for
Evaluating Frequency Compositions in Time Series",
author = "Omar Aguilar",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
year = "1996",
note = "Discussion Paper 96-22",
URL = "ftp://ftp.isds.duke.edu/pub/WorkingPapers/96-22.ps",
}
@InProceedings{al-li:application,
title = "Application of shift-invariant wavelet transform to
video coding",
author = "Mohammed A. Al-Mohimeed and Ching-Chung Li",
pages = "64--75",
booktitle = "Video Techniques and Software for Full-Service
Networks",
editor = "Tzi-cker Chiueh and Andrew G. Tescher",
volume = "2915",
series = "Proceedings of the SPIE",
year = "1997",
abstract = "The standard discrete wavelet transform lacks
translation invariance in 1-D signals and 2-D images.
The down-sampling at each coarser scale accentuates the
undesirable effects of the shift-variance, in
particular, on the motion estimation from decomposed
subimages in video coding. In this paper, we present a
study of applying the Chui-Shi shift-invariant wavelet
transform using 'oversampling frames' to video
compression. Further, we present an algorithm for
approximating the motion fields at different scales and
different frequency bands by utilizing the
multiresolution structure of wavelet decomposition.
Motion vectors at a higher resolution are predicted by
the motion vectors at a lower resolution through a
proper scaling. Experimental results on a salesman
video sequence show that the use of the 2-D
oversampling algorithm of a biorthogonal spline wavelet
has reduced the required number of motion vectors while
maintaining an acceptable prediction error when
compared to the classical block matching technique
using the standard wavelet transform. The proposed
approach will advance the video compression methodology
for applications to HDTV and video conferencing.",
}
@Book{ald-uns:medicine,
title = "Wavelets in Medicine and Biology",
booktitle = "Wavelets in Medicine and Biology",
author = "Akram Aldroubi and Michael Unser",
publisher = "CRC Press Inc.",
address = "Boca Raton",
pages = "608",
year = "1996",
ISBN = "0-8493-9483-X",
URL = "http://www.crcpress.com/prods/9483.htm",
abstract = "Considerable attention from the international
scientific community is currently focused on the wide
ranging applications of wavelets. For the first time,
the field's leading experts have come together to
produce a complete guide to wavelet transform
applications in medicine and biology. Wavelets in
Medicine and Biology provides accessible, detailed, and
comprehensive guidelines for all those interested in
learning about wavelets and their applications to
biomedical problems. The book consists of four main
sections: Theory and Implementation of Wavelet
Transforms, Wavelets in Medical Imaging and Tomography,
Wavelets and Biomedical Signal Processing, Wavelets and
Mathematical Models in Biology. The introductory
material is written for non-experts and includes basic
discussions of the theoretical and practical
foundations of wavelet methods. The background and
introduction is followed by contributions from the most
prominent researchers in the field, giving the reader a
complete survey of the use of wavelets in biomedical
engineering. An international perspective is provided
throughout the book, with contributions from experts
from Germany, France, America, Belgium, Holland,
Turkey, and Switzerland.",
}
@TechReport{all-tet:checking,
title = "Checking for Model Consistency in Optimal
Fingerprinting",
author = "M. R. Allen and S. F. B. Tett",
number = "RAL-TR-97-040",
institution = "Council for the Central Laboratory of the Research
Councils",
year = "1997",
}
@Article{and-tre:trends,
title = "Using Wavelets to Detect Trends",
author = "Edgar L. Andreas and George Trevi{\~n}o",
journal = JAOT,
volume = "14",
number = "3",
year = "1997",
pages = "554--564",
keywords = "",
abstract = "Wavelets are a new class of basis functions that are
finding wide use for analyzing and interpreting time
series data. This paper describes a new use for
wavelets--identifying trends in time series. The
general signal considered has a quadratic trend. The
inverted Haar wavelet and the elephant wavelet,
respectively, provide estimates of the first-order and
second-order coefficients in the trend polynomial.
Unlike usual wavelet applications, however, this
analysis requires only one wavelet dilation scale L,
where L is the total length of the time series. Error
analysis shows that wavelet trend detection is roughly
half as accurate as least squares trend detection when
accuracy is evaluated in terms of the mean-square error
in estimates of the first-order and second-order trend
coefficients. But wavelet detection is more than twice
as efficient as least squares detection in the sense
that it requires fewer than half the number of
floating-point operations of least squares regression
to yield the three coefficients of the quadratic trend
polynomial. This paper demonstrates wavelet trend
detection using artificial data and then various
turbulence data collected in the atmospheric surface
layer, and last, provides guidelines on when linear and
quadratic trends are ``significant'' enough to require
removal from a time series.",
}
@Article{and:magnitude,
title = "A Wavelet Magnitude Analysis Theorem",
author = "James C. Anderson",
journal = IEEETSP,
volume = "41",
number = "12",
year = "1993",
pages = "3541--3543",
abstract = "Wavelet transform is the constant-Q special case of
the generalized short time Fourier transform (GSTFT),
and is useful for wavelet analysis. Scalograms are
analyzed using specific types of filter/detector banks.
GSTFT results are universally applicable to wavelet
theory and are useful tools for scalogram sampling for
computation and data reduction functions.",
}
@Article{ans-gui-kai:lagrange,
title = "Wavelet Construction Using Lagrange Halfband Filters",
author = "R. Ansari and C. Guillemot and J. F. Kaiser",
journal = IEEETCS,
volume = "38",
number = "9",
year = "1991",
pages = "1116--1118",
abstract = "Using the approach described by M.J.T. Smith and T.P.
Barnwell (1986) for obtaining exact-reconstruction
filter banks, the authors present conjugate-quadrature
and linear-phase solutions for two-channel filter banks
using Lagrange halfband filters. It is shown that the
wavelet solutions obtained by I. Daubechies (1988)
under certain regularity conditions are the same as the
conjugate-quadrature solutions derived from Lagrange
halfband filters using the above approach. The
linear-phase solution that is described provides
filters with simple coefficients.",
}
@Article{ant-gij-gre:model,
title = "Model selection using wavelet decomposition and
applications",
author = "A. Antoniadis and I. Gijbels and G. Gr{\'e}goire",
journal = BKA,
volume = "84",
number = "4",
pages = "751--763",
year = "1997",
keywords = "consistency hypothesis testing minimum description
length criterion model selection nonparametric
regression wavelet decomposition",
abstract = "In this paper we discuss how to use wavelet
decompositions to select a regression model. The
methodology relies on a minimum description length
criterion which is used to determine the number of
nonzero coefficients in the vector of wavelet
coefficients. Consistency properties of the selection
rule are established and simulation studies reveal
information on the distribution of the minimum
description length selector. We then apply the
selection rule to specific problems, including testing
for pure white noise. The power of this test is
investigated via simulation studies and the selection
criterion is also applied to testing for no effect in
nonparametric regression.",
email = "Anestis.Antoniadis@imag.fr, gijbels@stat.ucl.ac.be,
Gerard.Gregoire@imag.fr",
}
@Article{ant-gij-mac:hazard,
title = "Nonparametric estimation for the location of a
change-point in an otherwise smooth hazard function
under random censoring",
author = "A. Antoniadis and I. Gijbels and B. MacGibbon",
journal = SJS,
volume = "",
number = "",
pages = "???--???",
year = "2000",
URL = "http://www.stat.ucl.ac.be/dp/dp98/dp9820.ps",
keywords = "",
abstract = ""
}
@Article{ant-gre-mck:curve,
title = "Wavelet Methods for Curve Estimation",
author = "A. Antoniadis and G. Gr{\'e}goire and
I. W. McKeague",
journal = JASA,
volume = "89",
number = "428",
pages = "1340--1353",
year = "1994",
keywords = "Nonparametric regression",
}
@Article{ant-gre-nas:density,
title = "Density and hazard rate estimation for right
censored data using wavelet methods",
author = "Anestis Antoniadis and G{\'e}rard Gr{\'e}goire and
Guy P. Nason",
journal = JRSSB,
volume = "61",
number = "1",
year = "1999",
pages = "63--84",
URL = "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/whf03.ps.gz",
keywords = "hazard rate survival data wavelet estimation",
abstract = "This paper describes a wavelet method for the
estimation of density and hazard rate functions from
randomly right-censored data. We adopt a
nonparametric approach in assuming that the density
and hazard rate have no specific parametric
form. The method is based on dividing the time axis
into a dyadic number of intervals and then counting
the number of events within each interval. The
number of events and the survival function of the
observations are then separately smoothed over time
via linear wavelet smoothers, and then the hazard
rate function estimators are obtained by taking the
ratio. We prove that the estimators have pointwise
and global mean-square consistency, obtain the best
possible asymptotic mean integrated squared error
convergence rate and are also asymptotically
normally distributed. We also describe simulation
experiments that show that these estimators are
reasonably reliable in practice. The method is
illustrated with two real examples. The first uses
survival time data for patients with liver
metastases from a colorectal primary tumour without
other distant metastases. The second is concerned
with times of unemployment for women and the wavelet
estimate, through its flexibility, provides a new
and interesting interpretation.",
}
@TechReport{ant-gij:abrupt,
title = "Detecting abrupt changes by wavelet methods",
author = "Anestis Antoniadis and Ir{\`e}ne Gijbels",
number = "9716",
institution = "Institute de Statistique, Universit{\'e} Catholique
de Louvain",
year = "1997",
URL = "http://www.stat.ucl.ac.be/dp/dp97/dp9716.ps",
note = "submitted to the {\em J. Nonpar. Stat.}",
}
@Article{ant-gus:wavelets,
title = "Wavelets and stochastic processes",
author = "Antoniou, I. and Gustafson, K.",
journal = "Mathematics and Computers in Simulation",
volume = "49",
number = "1-2",
year = "1999",
pages = "81--104",
abstract = "Wavelets are known to have intimate connections to
several other parts of mathematics, notably
phase-space analysis of signal processing,
reproducing kernel Hilbert spaces, coherent states
in quantum mechanics, spline approximation theory,
windowed Fourier transforms, and filter banks. Here,
we establish and survey a new connection, namely to
stochastic processes. Key to this link are the
Kolmogorov systems of ergodic theory.",
}
@Article{ant-pha:irregular,
title = "Wavelet regression for random or irregular design",
author = "Anestis Antoniadis and Dinh Tuan Pham",
journal = CSDA,
volume = "28",
number = "4",
year = "1998",
pages = "353--369",
abstract = "In this paper, wavelet regression estimators are
introduced, both in the random and the irregular
design cases and without the restriction that the
sample size be a power of two. A fast computational
algorithm for approximating the empirical
counterpart of the scaling and wavelet coefficients
is developed. The convergence rate of the estimator
is established. The method is illustrated by some
simulations and by a real example.",
}
@InCollection{ant:change-point,
title = "Wavelet estimators for change-point regression
models",
author = "Anestis Antoniadis",
booktitle = "Spline Functions and the Theory of Wavelets",
editor = "Serge Dubuc and Gilles Deslauriers",
volume = "18",
series = "CRM Proceedings \& Lecture Notes",
publisher = "American Mathematical Society",
year = "1999",
pages = "335--346",
description = "This work is based on a series of thematic workshops
on the theory of wavelets and the theory of splines.
Important applications are included. The volume is
divided into four parts: Spline Functions, Theory of
Wavelets, Wavelets in Physics, and Splines and
Wavelets in Statistics. Part one presents the broad
spectrum of current research in the theory and
applications of spline functions. Theory ranges from
classical univariate spline approximation to an
abstract framework for multivariate spline
interpolation. Applications include scattered-data
interpolation, differential equations and various
techniques in CAGD. Part two considers two
developments in subdivision schemes; one for uniform
regularity and the other for irregular situations.
The latter includes construction of multidimensional
wavelet bases and determination of bases with a given
time frequency localization. In part three, the
multifractal formalism is extended to fractal
functions involving oscillating singularites. There
is a review of a method of quantization of classical
systems based on the theory of coherent states.
Wavelets are applied in the domains of atomic,
molecular and condensed-matter physics. In part four,
ways in which wavelets can be used to solve important
function estimation problems in statistics are shown.
Different wavelet estimators are proposed in the
following distinct cases: functions with
discontinuities, errors that are no longer Gaussian,
wavelet estimation with robustness, and error
distribution that is no longer stationary. Some of
the contributions in this volume are current research
results not previously available in monograph form.
The volume features many applications and interesting
new theoretical developments. Readers will find
powerful methods for studying irregularities in
mathematics, physics, and statistics.",
}
@Article{ant:review,
title = "Wavelets in statistics: a review (with discussion)",
author = "Anestis Antoniadis",
journal = JISS,
volume = "6",
number = "2",
year = "1999",
pages = "???--???",
}
@Article{arf:subdiurnal,
title = "On subdiurnal effects in earth rotation",
author = "Arfa-Kaboodvand, K. and Groten, E.",
journal = "Studia Geophysica et Geodaetica",
volume = "43",
number = "3",
pages = "275--283",
year = "1999",
}
@TechReport{ari-vid:scalograms,
title = "On Wavelet Scalograms and Their Applications in
Economic Time Series",
author = "Miguel A. {Ari\~{n}o} and Brani Vidakovic",
number = "95-21",
year = "1995",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
URL = "ftp://ftp.isds.duke.edu/pub/Users/brani/papers/WavTS.ps",
}
@TechReport{ari:forecasting,
title = "Time Series Forcasts Via Wavelets: {A}n Application
to Car Sales in the {S}panish Market",
author = "Miguel A. {Ari\~{n}o}",
number = "95-30",
year = "1995",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
URL = "ftp://ftp.isds.duke.edu/pub/WorkingPapers/95-30.ps",
}
@Article{aro:two-normal,
title = "The probability function of the product of two normally
distributed variables",
author = "Leo A. Aroian",
journal = AofMS,
volume = "18",
pages = "265--271",
year = "1947",
}
@Article{bai-sap-pow-krz:underwater,
title = "Signal detection in underwater sound using wavelets",
author = "T. C. Bailey and T. Sapatinas and K. J. Powell and
W. J. Krzanowski",
journal = JASA,
volume = "93",
pages = "73--83",
year = "1998",
URL = "http://www.stats.bris.ac.uk/~mafs/jasa98_draft.ps.gz",
keywords = "Multivariate density estimation; Segmentation;
Short-time Fourier transform; Signal detection;
Signal processing; Thresholding; Underwater sounds;
Wavelet decomposition",
abstract = "This article considers the use of wavelet methods in
relation to a common signal processing problem, that
of detecting transient features in sound recordings
that contain interference or distortion. In this
particular case, the data are various types of
underwater sounds, and the objective is to detect
intermittent departures (potential `signals') from
the background sound environment in the data
(`noise'), where the latter may itself be evolving
and changing over time. We develop an adaptive model
of the background interference, using recursive
density estimation of the joint distribution of
certain summary features of its wavelet
decomposition. Observations considered to be
outliers from this density estimate at any time are
then flagged as potential `signals.' The performance
of our method is illustrated on artificial data,
where a known `signal' is contaminated with
simulated underwater `noise' using a range of
different signal-to-noise ratios, and a `baseline'
comparison is made with results obtained from a
relatively unsophisticated, but commonly used,
time-frequency approach. A similar comparison is
then reported in relation to the more significant
problem of detecting various types of dolphin sound
in real conditions.",
}
@Article{bal-oli-bau:discovery,
title = "Discovery of the near 158 day periodicity in group
sunspot numbers during the eighteenth century",
author = "Ballester, J. L. and Oliver, R. and Baudin, F.",
journal = ApJ,
volume = "522",
number = "2",
year = "1999",
pages = "L153--L156",
abstract = "A new record of solar activity, made by compiling
the daily number of sunspot groups visible on the
Sun's surface between 1610 and 1995, has recently
been made available by Hoyt and Schatten. Wavelet
analysis of this record shows that an episode of the
periodicity near 158 days occurred during the
eighteenth century, around the maximum of solar
cycle 2, and that episodes of the periodicity, much
weaker than that in solar cycle 2, have appeared
around the maxims of solar cycles 16-21 (covering
the interval 1923-1986). The presence of the
periodicity in the group sunspot number confirms
that it is caused by a periodic emergence of
magnetic flux. On the other hand, periodogram
analysis allows one to compare the behavior of the
periodicity in both sunspot groups and sunspot
areas, and the results suggest that, at least during
the twentieth century, the periodic emergence of
magnetic flux has adopted two different forms. In
solar cycles 16 and 17, new sunspot groups were
periodically formed, simultaneously increasing
the number of sunspot groups and the total sunspot
area on the Sun's surface, while during solar cycles
18, 19, 20, and 21 the periodicity has occurred
within already formed sunspot groups, increasing
sunspot areas only. We point out that this second
type of emergence, which enhances the magnetic
complexity of sunspot groups, is responsible for the
appearance of the periodicity in high-energy solar
flares as detected by the Solar Maximum Mission
during solar cycle 21.",
}
@InProceedings{bao-erd-che:scale,
title = "Scale-translation filtering for wideband correlated
noise attenuation",
author = "F. Bao and N. Erdol and Z. Chen",
pages = "652--660",
crossref = "szu:wavelet2",
abstract = "A novel idea of scale-translation filtering based on
the orthonormal wavelet transform is developed and
demonstrated.",
keywords = "scale-translation filtering. wideband correlated noise
attenuation. orthonormal wavelet transform.",
}
@InProceedings{bao-erd:discrete,
title = "{O}n the discrete wavelet transform and shiftability",
author = "Bao. Feng and N. Erdol",
booktitle = "Conference Record of the Twenty-Seventh Asilomar
Conference on Signals, Systems and Computers",
volume = "2",
editor = "A. Singh",
year = "1993",
pages = "1442--1445",
note = "1-3 Nov. 1993, Pacific Grove, CA, USA",
abstract = "We analyze the relationship between the change that is
observed in the wavelet coefficients when a signal is
time shifted and the time and frequency distributions
of the wavelet functions. We address the effects of
shift variance and show how it can be useful.",
keywords = "discrete wavelet transform. wavelet coefficients. time
shifted signal. frequency distribution. time
distribution. wavelet functions. shift variance.",
}
@InProceedings{bao-erd:optimal,
title = "{T}he optimal wavelet transform and translation
invariance",
booktitle = "IEEE International Conference on Acoustics, Speech and
Signal Processing",
volume = "3",
pages = "13--16",
year = "1994",
author = "F. Bao and N. Erdol",
note = "19-22 April 1994, Adelaide, SA, Australia",
abstract = "Orthonormal wavelet representations are known to be
time-variant. With shifting of the input signal, the
energy distribution in time-scale plane also changes.
We define the `separability' of a wavelet function both
in the scale and translation domains as a measure of
its localization with respect to translation. We derive
a criterion for the optimal initial phase and then
develop an algorithm for its choice in the case of
stationary and nonstationary signals.",
keywords = "optimal wavelet transform. orthonormal wavelet
representations. input signal shifting. energy
distribution. wavelet function separability.
translation domain. scale domain. translation
invariance. optimal initial phase. algorithm.
nonstationary signals. stationary stationary signals.
time-frequency transform. time-variant
representation.",
}
@Article{bas-etal:modeling,
title = "Modeling and estimation of multiresolution stochastic
processes",
author = "M. Basseville and A. Benveniste and K. C. Chou and S.
A. Golden and R. Nikoukhah and A. S. Willsky",
journal = IEEETIT,
volume = "38",
number = "2",
year = "1992",
pages = "766--784",
keywords = "multiscale statistical signal processing, data fusion,
estimation, multiresolution stochastic processes, image
processing, wavelet transform, modeling paradigm,
dynamic models, multiscale stationarity, homogeneous
trees, covariance kernels",
abstract = "An overview is provided of the several components of a
research effort aimed at the development of a theory of
multiresolution stochastic modeling and associated
techniques for optimal multiscale statistical signal
and image processing. A natural framework for
developing such a theory is the study of stochastic
processes indexed by nodes on lattices or trees in
which different depths in the tree or lattice
correspond to different spatial scales in representing
a signal or image. In particular, it is shown how the
wavelet transform directly suggests such a modeling
paradigm. This perspective then leads directly to the
investigation of several classes of dynamic models and
related notions of multiscale stationarity in which
scale plays the role of a time-like variable. The
investigation of models on homogeneous trees is
emphasized. The framework examined here allows for
consideration, in a very natural way, of the fusion of
data from sensors with differing resolutions. Also,
thanks to the fact that wavelet transforms do an
excellent job of 'compressing' large classes of
covariance kernels, it is seen that these modeling
paradigms appear to have promise in a far broader
context than one might expect.",
}
@InProceedings{bay-bar:multiple,
title = "Multiple Window Time-Frequency Analysis",
author = "Metin Bayram and Richard G. Baraniuk",
booktitle = "Proceedings of the IEEE-SP International Symposium
on Time-Frequency and Time-Scale Analysis",
pages = "173--176",
year = "1996",
keywords = "multiple window time-frequency analysis robust
method time-varying spectrum estimation
nonstationary random process time-scale planes
Thomson's method wavelet functions statistical test
chirping line components stationary signals",
abstract = "We propose a robust method for estimating the
time-varying spectrum of a non-stationary random
process. Our approach extends Thomson's powerful
multiple window spectrum estimation scheme to the
time-frequency and time-scale planes. The method
refines previous extensions of Thomson's method
through optimally concentrated window and wavelet
functions and a statistical test for extracting
chirping line components.",
}
@TechReport{bay-bar:multiple2,
title = "Multiple Window Time-Varying Spectrum Estimation",
author = "Metin Bayram and Richard G. Baraniuk",
institution = "Isaac Newton Institute program on Nonlinear and
Nonstationary Signal Analysis",
year = "1999",
abstract = "We overview a new non-parametric method for
estimating the time-varying spectrum of a
non-stationary random process. Our method extends
Thomson's powerful multiple window spectrum
estimation scheme to the time-frequency and
time-scale planes. Unlike previous extensions of
Thomson's method, we identify and utilize optimally
concentrated Hermite window and Morse wavelet
functions and develop a statistical test for
extracting chirping line components. Examples on
synthetic and real-world data illustrate the
superior performance of the technique.",
}
@Article{bel-wan:symmetric,
title = "Compactly supported orthogonal symmetric scaling
functions",
author = "Belogay, E. and Wang, Y.",
journal = ACHA,
volume = "7",
number = "2",
year = "1999",
pages = "137--150",
abstract = "Daubechies (1988, Comm. Pure Appl. Math. 41,
909-996) showed that, except for the Hear function,
there exist no compactly supported orthogonal
symmetric scaling functions for the dilation q =
2. Nevertheless, such scaling functions do exist for
dilations q > 2 (as evidenced by Chui and Lien's
construction (1995, Appl. Comput. Harmon. Anal. 2,
68-84) for q = 3); these functions are the main
object of this paper. We construct new symmetric
scaling functions and introduce the ``Batman''
family of continuous symmetric scaling functions
with very small supports. We establish the exact
smoothness of the ```Batman'' scaling functions
using the joint spectral radius technique.",
}
@Book{ben-fra:wavelets,
title = "Wavelets: Mathematics and Applications",
editor = "John J. Benedetto and Michael W. Frazier",
publisher = "CRC Press",
address = "Boca Raton",
year = "1994",
pages = "575",
loc = "QA403.3 .W4 1994",
}
@Article{ben-hoc:fdr,
title = "Controlling the False Discovery Rate: {A} Practical
and Powerful Approach to Multiple Testing",
author = "Yoav Benjamini and Yosef Hochberg",
journal = JRSSB,
volume = "57",
number = "1",
year = "1995",
pages = "289--300",
abstract = "The common approach to the multiplicity problem calls
for controlling the familywise error rate (FWER). This
approach, though, has faults, and we point out a few. A
different approach to problems of multiple significance
testing is presented. It calls for controlling the
expected proportion of falsely rejected hypotheses the
false discovery rate. This error rate is equivalent to
the FWER when all hypotheses are true but is smaller
otherwise. Terefore, in problems where the control of
the false discovery rate rather than that of the FWER
is desired, there is potential for a gain in power. A
simple sequential Bonferroni-type procedure is proved
to control the false discovery rate for independent
test statistics, and a simulation study shows that the
gain in power is substantial. The use of the new
procedure and the appropriateness of the criterion are
illustrated with examples.",
keywords = "Bonferroni-type procedures Familywise error rate
Multiple-comparison procedures p-values",
}
@InProceedings{bey-etal:SAR,
title = "{SAR} imaging and multiresolution analysis",
author = "Beylkin, G. and Gorman, J. D. and Li-Fliss, S. and
Ricoy, M. A.",
booktitle = "Algorithms for Synthetic Aperture Radar Imagery II",
series = "Proceedings of the SPIE",
volume = "2487",
year = "1995",
pages = "144--152",
keywords = "SAR imaging multiresolution analysis synthetic
aperture radar image formation algorithms
unequally-spaced FFT USFFT algorithm complexity
computational cost multiresolution SAR imaging image
reconstruction",
abstract = "Many synthetic aperture radar (SAR) image formation
algorithms require the computation of a
multidimensional Fourier transform of
irregularly-sampled or unequally-spaced data
samples. We apply a recently developed algorithm,
the unequally-spaced FFT (USFFT) (Beylkin, 1995), to
SAR image formation and compare its accuracy and
complexity to a conventional algorithm. We find that
the USFFT algorithm allows comparable accuracy to
traditional approaches at a slightly reduced
computational cost. We briefly discuss extensions of
the USFFT algorithm to multiresolution SAR imaging.",
}
@InProceedings{bey-sai:autocorrelation,
title = "Wavelets, their autocorrelation functions, and
multiresolution representation of signals",
author = "Gregory Beylkin and Naoki Saito",
booktitle = "Intelligent Robots and Computer Vision XI:
Biological, Neural Net and 3-D Methods",
series = "Proceedings of the SPIE",
volume = "1826",
year = "1992",
pages = "39--50",
keywords = "compactly supported wavelets, autocorrelation
functions, multiresolution signal representation,
iterative interpolation schemes, dilations,
translations, auto-correlation shell, signal
analysis",
URL = "ftp://amath-ftp.colorado.edu/pub/wavelets/papers/spie.ps.Z",
abstract = "We summarize the properties of the auto-correlation
functions of compactly supported wavelets, their
connection to iterative interpolation schemes, and
the use of these functions for multiresolution
analysis of signals. We briefly describe properties
of representations using dilations and translations
of these auto-correlation functions (the
auto-correlation shell) which permit multiresolution
analysis of signals.",
}
@Article{bey:representation,
title = "On the representation of operators in bases of
compactly supported wavelets",
author = "G. Beylkin",
journal = SINUM,
volume = "29",
year = "1992",
pages = "1716--1740",
}
@Book{bic-dok:basic-ideas,
title = "Mathematical Statistics: Basic Ideas and Selected
Topics",
author = "Peter J. Bickel and Kjell A. Doksum",
publisher = "Holden-Day, Inc.",
address = SF,
pages = "492",
year = "1977",
}
@TechReport{bie-vid:adaptive,
title = "Time Adaptive Wavelet Denoising",
author = "Concha Bielza and Brani Vidakovi\'{c}",
year = "1996",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
URL = "ftp://ftp.isds.duke.edu/pub/Users/brani/papers/Timeadapt.ps",
}
@Article{bij-sle-rue-leg:universe,
journal = PIEEE,
volume = "84",
number = "4",
year = "1996",
pages = "670--679",
title = "{W}avelets and the study of the distant universe",
author = "A. Bijaoui and E. Slezak and F. Rue and E. Lega",
abstract = "The large-scale distribution of galaxies in the
Universe exhibits structures at various scales, these
so-called groups, clusters, and superclusters of
galaxies being more or less hierarchically organized. A
specific vision model is needed in order to detect,
describe, and classify each component of this
hierarchy. To do so rue have developed a multiscale
vision model based on an unfolding into a scale space
allowing us to detect structures of different sizes. A
discrete wavelet transform is done by the a trous
algorithm. The algorithm is implemented for
astronomical images and also for lists of object
positions, currently called catalogues in astronomical
literature. Some applications on astrophysical data of
cosmological interest are briefly described: 1)
inventory procedures for galaxy counts on wide-field
images, 2) processing of X-ray cluster images, leading
to the analyses of the total matter distribution, and
3) detection of large-scale structures from galaxy
counts. From the analyses of n-body simulations we show
that the vision model from the wavelet transform
provides a new statistical indicator on cosmological
scenarios.",
keywords = "transform. clusters",
}
@Unpublished{bij-sta-mur:atrous,
title = "Restauration des Images Multi-Echelles par
l'{A}lgorithme \`{a} Trous",
author = "Albert Bijaoui and Jean-Luc Starck and Fionn Murtagh",
year = "1994",
note = "In French",
URL = "http://http.hq.eso.org/~fmurtagh/papers/trait-sig-94.ps",
}
@Book{bil:probability68,
title = "Convergence of Probability Measures",
author = "P. Billingsley",
year = "1968",
publisher = "John Wiley \& Sons",
address = NY,
}
@Article{bra-mci:climate,
title = "Determining climate-induced patterns using wavelet
analysis",
author = "G. A. Bradshaw and B. A. McIntosh",
journal = EP,
volume = "83",
year = "1994",
pages = "133--142",
abstract = "A method using wavelet analysis is introduced for the
purpose of identifying and isolating inferred climatic
components of the hydrologic record. This method
affords an informed procedure for choosing filter
dimensions for the purpose of signal decomposition.",
}
@Article{bra-spi:canopy,
title = "Characterizing canopy gap structure in forests using
wavelet analysis",
author = "G. A. Bradshaw and Thomas A. Spies",
journal = JEcol,
volume = "80",
number = "2",
year = "1992",
pages = "205--215",
keywords = "forest ecology, plant canopies, spatial analysis,
statistics",
abstract = "1. The wavelet transform is introduced as a technique
to identify spatial structure in transect data. Its
main advantages over other methods of spatial a nalysis
are its ability to preserve and display hierarchical
information while allowing for pattern decomposition.
2. Two applications are presented: simple
one-dimensional simulations and a set of 200-m transect
data of canopy opening measurements taken in 12 stands
dominated by Pseudotsuga menziesii ranging over three
developmental stages. 3. The calculation of the wavelet
variance, derived from the transform, facilitates
comparison based on dominant scale of pattern between
multiple datase ts such as the stands described. 4. The
results of the analysis indicate that while canopy
pattern trends follow stand development, small to
intermediate disturbances significantly influence
canopy structure.",
}
@Unpublished{bre-liu-tor:monsoon,
title = "Intraseasonal oscillations off Monterey, CA",
author = "L. Breaker and P. Liu and C. Torrence",
year = "1998",
note = "National Center for Atmospheric Research",
URL = "http://www.cgd.ucar.edu/~torrence/liu/",
abstract = "",
}
@Article{bre:heuristics,
title = "Heuristics of instability and stabilization in model
selection",
author = "L. Breiman",
journal = AofS,
volume = "24",
year = "1996",
pages = "2350--2383",
}
@Unpublished{bri-chi-iri-mor:markov-chain,
title = "Some Wavelet-Based Analyses of Markov Chain Data",
author = "David R. Brillinger and Chang Chiann and Rafael
A. Irizarry and Pedro A. Morettin",
year = "1998",
note = "Version 5.0",
}
@Article{bri-hen:multigrid,
title = "Wavelets and Multigrid",
author = "William L. Briggs and Van Emden Henson",
journal = SIAMJSC,
volume = "14",
number = "2",
year = "1993",
pages = "506--510",
URL = "http://www-math.cudenver.edu/~wbriggs/psfiles/briggs_henson_93.ps",
}
@Article{bri:cumulants,
title = "Some Uses of Cumulants in Wavelet Analysis",
author = "David R. Brillinger",
journal = "Nonparametric Statistics",
volume = "6",
year = "1996",
pages = "93--114",
}
@InProceedings{bri:point-processes,
title = "Some Wavelet Analysis of Point Process Data",
author = "David R. Brillinger",
booktitle = "Thirty-First Asilomar Conference on Signals, Systems
and Computers",
year = "1997",
pages = "93--114",
}
@Article{bro:distribution,
title = "The Distribution Function of Positive Definite
Quadratic Forms in Normal Random Variables",
author = "Robert H. Brown",
journal = SIAMJSSC,
volume = "7",
pages = "689--695",
year = "1986",
keywords = "Analysis of variance; Unbalanced ANOVA design;
Laguerre polynomial",
}
@Article{bro:quantitative,
title = "Quantitative convergence assessment for {M}arkov
chain {M}onte {C}arlo via cusums",
author = "S. P. Brooks",
journal = SC,
volume = "8",
number = "3",
year = "1998",
pages = "267--274",
}
@Article{bru-don-gao:wavelet,
title = "Wavelet analysis [for signal processing]",
author = "Andrew Bruce and David Donoho and Hong-Ye Gao",
journal = IEEES,
volume = "33",
number = "10",
year = "1996",
pages = "26--35",
abstract = "As every engineering student knows, any signal can be
portrayed as an overlay of sinusoidal waveforms of
assorted frequencies. But while classical analysis
copes superbly with naturally occurring sinusoidal
behavior-the kind seen in speech signals-it is
ill-suited to representing signals with
discontinuities, such as the edges of features in
images. Latterly, another powerful concept has swept
applied mathematics and engineering research: wavelet
analysis. In contrast to a Fourier sinusoid, which
oscillates forever, a wavelet is localized in time-it
lasts for only a few cycles. Like Fourier analysis,
however, wavelet analysis uses an algorithm to
decompose a signal into simpler elements. Here, the
authors describe how localized waveforms are powerful
building blocks for signal analysis and rapid
prototyping-and how they are now available in software
toolkits.",
}
@Book{bru-gao:book,
title = "Applied Wavelet Analysis with {S-PLUS}",
author = "Andrew Bruce and Hong-Ye Gao",
year = "1996",
publisher = "Springer",
address = NY,
ISBN = "0-387-94714-0",
URL = "http://www.springer-ny.com/catalog/np/jul96np/DATA/0-387-94714-0.html",
abstract = "This book introduces applied wavelet analysis through
the S-PLUS software system. Using a visual data
analysis approach, wavelet concepts are explained in a
way that is intuitive and easy to understand. In
addition to wavelets, a whole range of related signal
processing techniques such as wavelet packets, local
cosine analysis, and matching pursuits are covered.
Applications of wavelet analysis are illustrated,
including nonparametric function estimation, digital
image compression, and time-frequency signal analysis.
The book and software is intended for a broad range of
data analysts, scientists, and engineers. While most
textbooks on wavelet analysis require advanced training
in mathematics, this book minimizes reliance on formal
mathematical methods. Readers should be familiar with
calculus and linear algebra at the undergraduate
level.",
}
@Article{bru-gao:waveshrink,
title = "Understanding {W}ave{S}hrink: {V}ariance and Bias
Estimation",
author = "Andrew Bruce and Hong-Ye Gao",
journal = BKA,
volume = "83",
number = "4",
year = "1996",
URL = "ftp://ftp.statsci.com/pub/gao/varbias.ps.Z",
keywords = "Bias and Variance Estimation; Confidence Interval;
Hard and Soft Shrink; Non-parametric Regression; Signal
De-noising; Threshold Selection; Wavelet Transform;
WaveShrink",
abstract = "Donoho and Johnstone's WaveShrink procedure has proven
valuable for signal de-noising and non-parametric
regression. WaveShrink is based on the principle of
shrinking wavelet coefficients towards zero to remove
noise. WaveShrink has very broad asymptotic
near-optimality properties. In this paper, we derive
computationally efficient formulas for computing the
exact bias, variance and $L_2$ risk of WaveShrink
estimates in finite sample situations. These formulas
provide a new way of understanding how WaveShrink
works, what its limitations are, and the pros and cons
of the shrinkage schemes: {\em soft} shrink vs. {\em
hard} shrink. It complements the tools of simulation
and asymptotic analysis. We use these formulas to
estimate the bias, the variance and the $L_2$ risk for
WaveShrink. Variance estimates are used to construct
approximate pointwise confidence intervals and applied
to synthetic and real examples. We also address the
problem of threshold selection, computing minimax
thresholds and ideal thresholds for both hard and soft
shrinkage.",
}
@Article{bru-gao-stu:subset,
title = "Subset-selection and ensemble methods for wavelet
de-noising",
author = "Andrew Bruce and Hong-Ye Gao and Werner Stuetzle",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "167--182",
keywords = "cycle spinning model combination nonparametric
regression stepwise regression wavelet shrinkage",
abstract = "Many nonparametric regression procedures are based
on ``subset selection'': they choose a subset of
carriers from a large or even infinite set, and then
determine the coefficients of the chosen carriers by
least squares. Procedures which can be cast in this
framework include Projection Pursuit, Turbo, Mars,
and Matching Pursuit. Recently, considerable
attention has been given to ``ensemble estimators''
which combine least squares estimates obtained from
multiple subsets of carriers. In the parametric
regression setting, such ensemble estimators have
been shown to improve on the accuracy of subset
selection procedures in some situations. In this
paper we compare subset selection estimators and
ensemble estimators in the context of wavelet
de-noising. We present simulation results
demonstrating that a certain class of ensemble
wavelet estimators, based on the concept of ``cycle
spinning'', are significantly more accurate than
subset selection methods. These advantages hold even
when the subset selection procedures can rely on an
oracle to select the optimal number of carriers. We
compute ideal thresholds for translation invariant
wavelet shrinkage and investigate other approaches
to ensemble wavelet estimation.",
}
@Book{bur-gop-guo:book,
title = "Introduction to Wavelets and Wavelet Transforms: A
Primer",
author = "C. Sidney Burrus and Ramesh A. Gopinath and Haitao
Guo",
year = "1998",
publisher = "Prentice Hall",
address = NJ,
ISBN = "0-13-489600-9",
URL = "http://www-dsp.rice.edu/wavebook",
abstract = "This primer presents a well balanced blend of the
mathematical theory underlying wavelet techniques
and a discussion that gives insight into why
wavelets are successful in signal analysis,
compression, dection, numerical analysis, and a wide
variety of other theoretical and practical
applications. It fills a gap in the existing wavelet
literature with its unified view of expansions of
signals into bases and frames, as well as the use of
filter banks as descriptions and algorithms.",
}
@Article{bur-etal:spatio,
title = "{A} wavelet multiresolution analysis for
spatio-temporal signals",
author = "T. J. Burns and S. K. Rogers and M. E. Oxley and
D. W. Ruck",
journal = IEEETAES,
volume = "32",
number = "2",
year = "1996",
pages = "628--649",
abstract = "The wavelet filters of the conventional 3D
multiresolution analysis possess homogeneous spatial
and temporal frequency characteristics which Limits
one's ability to match filter frequency
characteristics to signal frequency behavior. Also,
the conventional 3D multiresolution analysis employs
an oct-tree decomposition structure which restricts
the analysis of signal details to identical
resolutions in space and time. This paper presents a
3D wavelet multiresolution analysis constructed from
nonhomogeneous spatial and temporal filters, and an
orthogonal sub-band coding scheme that decouples the
spatial and temporal decomposition processes.",
}
@Article{bur-wil-nas:impact,
title = "Impact during equine locomotion: {T}echniques for
measurement and analysis",
author = "J. F. Burn and A. M. Wilson and G. P. Nason",
journal = "Equine Veterinary Journal",
volume = "23",
year = "1997",
pages = "9--12",
}
@TechReport{bus-len:numerical,
title = "Numerical tests for bivariate wavelet schemes",
author = "R. Buschini and L. Lenarduzzi",
number = "IAMI 97.5",
year = "1997",
institution = "Instituto per le Applicazioni della Matematica e
dell'Informatica",
}
@Article{cai-bro:nonequispaced,
title = "Wavelet Shrinkage for Nonequispaced Samples",
author = "T. Tony Cai and Lawrence D. Brown",
journal = AofS,
volume = "26",
number = "5",
year = "1998",
pages = "1783--1799",
URL = "http://www.stat.purdue.edu/people/tcai/paper/noneq.ps",
keywords = "wavelets multiresolution approximation nonparametric
regression minimax adaptivity piecewise Holder
class",
abstract = "Standard wavelet shrinkage procedures for
nonparametric regression are restricted to
equispaced samples. There, data are transformed into
empirical wavelet coefficients and threshold rules
are applied to the coefficients. The estimators are
obtained via the inverse transform of the denoised
wavelet coefficients. In many applications, however,
the samples are nonequispaced. It can be shown that
these procedures would produce suboptimal estimators
if they were applied directly to nonequispaced
samples. We propose a wavelet shrinkage procedure
for nonequispaced samples. We show that the estimate
is adaptive and near optimal. For global estimation,
the estimate is within a logarithmic factor of the
minimax risk over a wide range of piecewise Holder
classes, indeed with a number of discontinuities
that grows polynomially fast with the sample
size. For estimating a target function at a point,
the estimate is optimally adaptive to unknown degree
of smoothness within a constant. In addition, the
estimate enjoys a smoothness property: if the target
function is the zero function, then with probability
tending to 1 the estimate is also the zero
function.",
}
@Article{cai-hur-tsa:score,
title = "Score tests for heteroscedasticity in wavelet
regression",
author = "Z. W. Cai and C. M. Hurvich and C. L. Tsai",
journal = BKA,
volume = "85",
number = "1",
pages = "229--234",
year = "1998",
keywords = "de-noising. signal extraction. thresholding",
abstract = "We consider two Score tests for heteroscedasticity in
the errors of a signal;plus-noise model, where the
signal is estimated;by wavelet thresholding methods.
The error variances are assumed to depend on observed
covariates, through a parametric relationship of known
form. The tests are based on the approaches of Breusch
& Pagan (1979) and Koenker (1981). We establish the
asymptotic validity of the tests and examine their
performance in a simulation study. The Koenker test is
found to perform well, in terms of both size and
power.",
}
@TechReport{cai-sil:incorporating,
title = "Incorporating Information on Neighboring Coefficients
into Wavelet Estimation",
author = "T. Tony Cai and Bernard W. Silverman",
institution = "Department of Statistics, Purdue University",
number = "98-13",
year = "1998",
URL = "http://www.stat.purdue.edu/people/tcai/NeighBlock/neighblock.ps",
}
@TechReport{cai:adaptivity,
title = "On Adaptivity of {B}lock{S}hrink Wavelet Estimator
Over {B}esov Spaces",
author = "T. Tony Cai",
institution = "Department of Statistics, Purdue University",
number = "97-05",
year = "1997",
URL = "http://www.stat.purdue.edu/people/tcai/paper/blockbesov.ps",
}
@TechReport{cai:minimax,
title = "Minimax Wavelet Estimation Via Block Thresholding",
author = "T. Tony Cai",
institution = "Department of Statistics, Purdue University",
number = "96-41",
year = "1996",
URL = "http://www.stat.purdue.edu/people/tcai/paper/blockmini.ps",
}
@Article{cam-mas:approximation,
title = "Wavelet approximation of deterministic and random
signals: convergence properties and rates",
author = "S. Cambanis and Elias Masry",
journal = IEEETIT,
volume = "40",
number = "4",
year = "1994",
pages = "1013--1029",
keywords = "convergence properties, convergence rates,
deterministic signals, wavelet approximation, signal
resolution, correlation function, stationary random
signals, nonstationary random signals, finite mean
energy, scale function, signal smoothness",
abstract = "The multiresolution decomposition of deterministic and
random signals and the resulting approximation at
increasingly finer resolution is examined.
Specifically, an nth-order expansion is developed for
the error in the wavelet approximation at resolution
$2^{-l}$ of deterministic and random signals. The
deterministic signals are assumed to have n continuous
derivatives, while the random signals are only assumed
to have a correlation function with continuous
nth-order derivatives off the diagonal-a very mild
assumption. For deterministic signals square integrable
over the entire real line, for stationary random
signals over finite intervals, and for nonstationary
random signals with finite mean energy over the entire
real line, the smoothness of the scale function can be
matched with the signal smoothness to substantially
improve the quality of the approximation. In sharp
contrast, this is feasible only in special cases for
nonstationary random signals over finite intervals and
for deterministic signals which are only locally square
integrable.",
}
@Unpublished{cap:denoised,
title = "Wavelet de-noised financial time series",
author = "Enrico Capobianco",
year = "1997",
note = "Department of Mathematical Modelling, Technical
University of Denmark",
URL = "http://eivind.imm.dtu.dk/staff/enrico/duke_enrico.ps",
}
@Unpublished{cap:feature-detection,
title = "Feature Detection with Matching Pursuit in High
Frequency Nonstationary Time Series",
author = "Enrico Capobianco",
year = "1999",
note = "Department of Mathematical Modelling, Technical
University of Denmark",
URL = "ftp://eivind.imm.dtu.dk/pub/300699a.ps.Z",
}
@Unpublished{cap:high-frequency,
title = "High Frequency Stock Returns Volatility: Feature
Extraction and Pattern Recognition via Wavelet
Transforms",
author = "Enrico Capobianco",
year = "1999",
note = "Department of Mathematical Modelling, Technical
University of Denmark",
URL = "",
}
@Unpublished{cap:volatility,
title = "Wavelet Transforms for the Statistical Analysis of
Returns Generating Stochastic Processes",
author = "Enrico Capobianco",
year = "1998",
note = "Department of Mathematical Modelling, Technical
University of Denmark",
URL = "http://eivind.imm.dtu.dk/staff/enrico/jedc.ps.Z",
}
@Unpublished{cap:wavelets,
title = "Wavelets for High Frequency Financial Time Series",
author = "Enrico Capobianco",
year = "1999",
note = "Department of Mathematical Modelling, Technical
University of Denmark",
email = "enrico@eivind.imm.dtu.dk",
URL = "http://eivind.imm.dtu.dk/staff/enrico/int99.ps.Z",
}
@InProceedings{car-hud:EEG-signals,
title = "Wavelet denoising of {EEG} signals and identification
of evokedresponse potentials",
author = "R{\'e}ne A. Carmona and Lonnie H. Hudgins",
pages = "91--104",
crossref = "lai-uns:wavelet2",
abstract = "The purpose of this study is to apply a recently
developed wavelet based de-noising filter to the
analysis of human electroencephalogram (EEG) signals,
and measure its performance. The data used contained
subject EEG responses to two different stimuli using
the `odd-ball' paradigm. Electrical signals measured at
standard locations on the scalp were processed to
detect and identify the Evoked Response Potentials
(ERP's). First, electrical artifacts emitting from the
eyes were identified and removed. Second, the mean
signature for each type of response was extracted and
used as a matched filter to define baseline detector
performance for the noisy data. Third, a nonlinear
filtering procedure based on the wavelet extrema
representation was used to de-noise the signals.
Overall detection rates for the de-noised signals were
then compared to the baseline performance. It was found
that while the filtered signals have significantly
lower noise than the raw signals, detector performance
remains comparable. We therefore conclude that all of
the information that is important to matched filter
detection is preserved by the filter. The implication
is that the wavelet based filter eliminates much of the
noise while retaining ERP's.",
URL = "",
}
@Book{car-hwa-tor:book,
title = "Practical Time-Frequency Analysis: Gabor and Wavelet
Transforms with an Implementation in S",
booktitle = "Practical Time-Frequency Analysis: Gabor and Wavelet
Transforms with an Implementation in S",
author = "Ren{\'e} A. Carmona and Wen L. Hwang and Brun
Torr{\'e}sani",
publisher = "Academic Press",
address = "San Diego",
series = "Wavelet Analysis and Its Applications",
volume = "9",
year = "1998",
}
@Article{car-hwa-tor:characterization,
title = "Characterization of Signals by the Ridges of Their
Wavelet Transforms",
author = "Ren{\'e} A. Carmona and Wen L. Hwang and Brun
Torr{\'e}sani",
journal = IEEETSP,
volume = "45",
number = "10",
pages = "2586--2590",
year = "1997",
URL = "ftp://chelsea.princeton.edu/pub/outgoing/signal/cht1.ps",
abstract = "We present a couple of new algorithmic procedures for
the detection of ridges in the modulus of the
(continuous) wavelet transform of one-dimensional (1-D)
signals, These detection procedures are shown to be
robust to additive white noise, We also derive and test
a new reconstruction procedure, The latter uses only
information from the restriction of the wavelet
transform to a sample of points from the ridge. This
provides a very efficient way to code the information
contained in the signal.",
}
@Article{car-etal:absolute,
title = "Absolute optimal time-frequency basis -- a research
tool",
author = "C{\^a}rsteanu, A. and Sapozhnikov, V. B. and
Venugopal, V. and Foufoula-Georgiou, E.",
journal = JPA,
volume = "30",
number = "20",
pages = "7133--7146",
year = "1997",
URL = "",
abstract = "The paper presents a method for finding the absolute
best basis out of the library of bases offered by
the wavelet packet decomposition of a discrete
signal. Data-adaptive optimality is achieved with
respect to an objective function, e.g. minimizing
entropy, and concerns the choice of the Heisenberg
rectangles tiling the time-frequency domain over
which the energy of the signal is distributed. It is
also shown how optimizing a concave objective
function is equivalent to concentrating maximal
energy into a few basis elements. Signal- adaptive
basis selection algorithms currently in use do not
generally find the absolute best basis, and moreover
have an asymmetric time-frequency
adaptivity-although a complete wavepacket
decomposition comprises a symmetric set of tilings
with respect to time and frequency. The higher
adaptivity in frequency than in time can lead to
ignoring frequencies that exist over short time
intervals (short as compared to the length of the
whole signal, not to the period corresponding to
these frequencies). Revealing short-lived
frequencies to the investigator can bring up
important features of the studied process, such as
the presence of coherent ('persistent') structures
in a time series.",
}
@InProceedings{car:transients,
title = "Wavelet identification of transients in noisy time
series",
author = "Ren{\'e} A. Carmona",
pages = "392--400",
crossref = "lai:wavelet1",
URL = "http://www.isds.duke.edu/~brani/wp/CarmonaTSTrans.ps",
keywords = "transients detection, wavelet identification, noisy
time series, signal analysis, denoising procedure,
wavelet transform, bootstrap, direct Monte Carlo
simulations, reconstruction algorithm",
abstract = "The detection of transients in noisy time series is an
important part of modern signal analysis because of the
importance of its civil and military applications. The
author presents a new denoising procedure, the output
of which gives a very reasonable guess for the
component of the input signal which was buried in
noise. The algorithm has two main components. The first
one concerns the identification of the main
characteristics of the noise component and of the
typical effects it has on the wavelet transform of the
input signal. This information is used to identify the
points in the time-scale space which cannot be extrema
of the wavelet transform, unless something else than
noise was present in the input signal. This is done by
bootstrap in general but direct Monte Carlo simulations
can be used when parametric knowledge on the
distribution of the noise is available. The second part
deals with the actual reconstruction of what is
believed to be the component of the input which is to
be identified. This part of the algorithm uses the
reconstruction procedure of Mallat and Zhong (1992) as
revised by the author (1992) the main novelty being the
fact that this procedure is fed with the set of points
in the time-scale plane which passed the trimming test
of the extrema of the wavelet transform. The author
illustrates the efficiency of the reconstruction
algorithm using the examples of transients used
previously by the author (1992).",
}
@Article{cha-ho:mra,
title = "Multiresolution analysis, its link to the discrete
parameter wavelet transform, and its initialization",
author = "Y. T. Chan and K. C. Ho",
journal = IEEETSP,
volume = "44",
number = "4",
year = "1996",
pages = "1001--1007",
keywords = "Filtering, Electronics, Signal processing",
abstract = "Two-scale wavelet equations are derived for equivalent
multiresolution analysis (MRA) detail parameters and
the discrete parameter (DP) wavelet transform
coefficients for a signal s(t). MRA initialization by
prefiltering its input signal s(n) obtains the
equivalence between the DP and MRA coefficients. MRA
gives the DP of a signal s(t) when s(n) are samples of
the inner product of s(t) and the scaling function. A
simulation example is presented to discuss the
prefiltering procedure's effectiveness.",
}
@TechReport{cha-lon:k-stationarity,
title = "K-stationarity and wavelets",
author = "Bing Cheng and Howell Tong",
number = "96-28",
institution = "Institute of Mathematics and Statistics, University
of Kent at Cantebury",
year = "1996",
URL = "ftp://ftp.ukc.ac.uk/pub/maths/reports/1996/28/28.ps.gz",
}
@Book{cha:basics,
title = "Wavelet Basics",
author = "Y. T. Chan",
publisher = "Kluwer Academic Publishers",
address = "Boston",
year = "1995",
pages = "134",
URL = "http://kapis.www.wkap.nl/kapis/CGI-BIN/WORLD/book.htm?0-7923-9536-0",
keywords = "Preface. 1. Introduction. 2. Principles of the Wavelet
Transform 3. Multiresolution Analysis, Wavelets and
Digital Filters. 4. Current Topics. References.
Index.",
abstract = "Since the study of wavelets is a relatively new area,
much of the research coming from mathematicians, most
of the literature uses terminology, concepts and proofs
that may, at times, be difficult and intimidating for
the engineer. Wavelet Basics has therefore been written
as an introductory book for scientists and engineers.
The mathematical presentation has been kept simple, the
concepts being presented in elaborate detail in a
terminology that engineers will find familiar.
Difficult ideas are illustrated with examples which
will also aid in the development of an intuitive
insight. Chapter 1 reviews the basics of signal
transformation and discusses the concepts of duals and
frames. Chapter 2 introduces the wavelet transform,
contrasts it with the short-time Fourier transform and
clarifies the names of the different types of wavelet
transforms. Chapter 3 links multiresolution analysis,
orthonormal wavelets and the design of digital filters.
Chapter 4 gives a tour d'horizon of topics of current
interest: wavelet packets and discrete time wavelet
transforms, and concludes with applications in signal
processing.",
}
@Article{che-don-sau:atomic,
title = "Atomic decomposition by basis pursuit",
author = "Chen, S. S. B. and Donoho, D. L. and Saunders,
M. A.",
journal = SIAMJSC,
volume = "20",
number = "1",
year = "1999",
pages = "33--61",
URL = "http://epubs.siam.org/sam-bin/getfile/SISC/articles/30401.ps",
keywords = "overcomplete signal representation denoising
time-frequency analysis time-scale analysis l 1 norm
optimization matching pursuit wavelets wavelet
packets cosine packetsinterior-point methods for
linear programming total variation denoising
multiscale edges",
abstract = "The time-frequency and time-scale communities have
recently developed a large number of overcomplete
waveform dictionaries- stationary wavelets, wavelet
packets, cosine packets, chirplets, and warplets, to
name a few. Decomposition into overcomplete systems
is not unique, and several methods for decomposition
have been proposed, including the method of frames
(MOF), Matching pursuit (MP), and, for special
dictionaries, the best orthogonal basis (BOB). Basis
Pursuit (BP) is a principle for decomposing a signal
into an ``optimal'' superposition of dictionary
elements, where optimal means having the smallest
l(1) norm of coefficients among all such
decompositions. We give examples exhibiting several
advantages over MOF, MP, and BOB, including better
sparsity and superresolution. BP has interesting
relations to ideas in areas as diverse as ill-posed
problems, in abstract harmonic analysis, total
variation denoising, and multiscale edge
denoising. BP in highly overcomplete dictionaries
leads to large-scale optimization problems. With
signals of length 8192 and a wavelet packet
dictionary, one gets an equivalent linear program of
size 8192 by 212,992. Such problems can be attacked
successfully only because of recent advances in
linear programming by interior-point methods. We
obtain reasonable success with a primal-dual
logarithmic barrier method and conjugate-gradient
solver.",
}
@MastersThesis{che:msthesis,
title = "Wavelet Analysis and Statistics of {CN} Tower Current
Waveforms",
author = "Ying Chen",
year = "1997",
pages = "93",
school = "Department of Electrical and Computer Engineering,
University of Western Ontario",
URL = "http://www.ee.ryerson.ca:8080/~yichen/thesis",
email = "yichen@ee.ryerson.ca",
abstract = "",
}
@Article{chi-kol-mcc:abws,
title = "Adaptive Bayesian Wavelet Shrinkage",
author = "Hugh A. Chipman and Eric D. Kolaczyk and Robert E.
McCulloch",
journal = JASA,
volume = "92",
number = "440",
pages = "1413--1421",
year = "1997",
URL = "http://galton.uchicago.edu/techreports/ABWS.ps.Z",
}
@Unpublished{chi-mor:estimation,
title = "Estimation of Time Varying Linear Systems",
author = "Chang Chiann and Pedro A. Morettin",
year = "1999",
note = "University of S\~{a}o Paulo, S\~{a}o Paulo, Brazil",
URL = "ftp://ftp.ime.usp.br/pub/morettin/lsystem.ps.Z",
abstract = "",
}
@Article{chi-mor:stationary,
title = "A Wavelet Analysis for Time Series",
author = "Chang Chiann and Pedro A. Morettin",
journal = JNS,
volume = "10",
number = "1",
year = "1999",
pages = "1-46",
email = "pam@ime.usp.br",
URL = "ftp://ftp.ime.usp.br/pub/morettin/wavespec.ps.Z",
keywords = "time series wavelets wavelet periodogram wavelet
spectrum wavelet transform",
abstract = "In this paper we develop a wavelet spectral analysis
for a stationary discrete process. Some basic ideas
on wavelets are given and the concept of wavelet
spectrum is introduced. Asymptotic properties of the
discrete wavelet transform of a sample of observed
values from the process are derived and the wavelet
periodogram is considered as an estimator of the
wavelet spectrum. Applications to real and simulated
series are given.",
}
@InProceedings{cho-bar:interpolation,
title = "Interpolation and denoising of nonuniformly sampled
data using wavelet-domain processing",
author = "Hyeokho Choi and Richard Baraniuk",
booktitle = "Proceedings of IEEE International Conference on
Acoustics, Speech and Signal Processing",
pages = "",
year = "1999",
URL = "http://www-dsp.rice.edu/publications/pub/choi99in.ps.Z",
}
@InProceedings{cho-bar:segmentation,
title = "Image segmentation using wavelet-domain
classification",
author = "Hyeokho Choi and Richard Baraniuk",
pages = "???--???",
crossref = "uns-ald-lai:wavelet7",
URL = "http://www-dsp.rice.edu/publications/pub/choi99im.ps.Z",
}
@InProceedings{cho-etal:complex,
title = "Hidden {M}arkov tree modelling of complex wavelet
transforms",
author = "Hyeokho Choi and Justin Romberg and Richard Baraniuk
and Nick Kingsbury",
booktitle = "Proceedings of IEEE International Conference on
Acoustics, Speech and Signal Processing",
year = "2000",
pages = "???--???",
URL = "http://www-dsp.rice.edu/publications/pub/choi00icassp.ps.Z",
}
@Book{chu:introduction,
title = "An Introduction to Wavelets",
author = "C. K. Chui",
volume = "1",
series = "Wavelet Analysis and its Applications",
year = "1992",
publisher = "Academic Press, Inc.",
ISBN = "0-12-174584-8",
keywords = "An Overview, Fourier Analysis, Wavelet Transforms and
Time-frequency Analysis, Cardinal Spline Analysis,
scaling functions and Wavelets, Cardinal Spline
Wavelets, Orthogonal Wavelets and Wavelet Packets",
abstract = "This is the first volume in the series WAVELET
ANALYSIS AND ITS APPLICATIONS. It is an introductory
treatise on wavelet analysis, with an emphasis on
spline wavelets and and time-frequency analysis. Among
the basic topics covered are time frequency
localization, intergral wavelet transforms, dyadic
wavelets, frames, spine wavelets, orthonormal wavelet
bases, and wavelet packets. Is is suitable as a
textbook for a beginning course on wavelet analysis and
is directed toward both mathematicians and engineers
who wish to learn about the subject.",
}
@Book{chu:theory,
title = "Wavelets: Theory, Algorithms, and Applications",
editor = "Charles K. Chui and Laura Montefusco and Luigia
Puccio",
volume = "5",
series = "Wavelet Analysis and its Applications",
year = "1994",
publisher = "Academic Press, Inc.",
ISBN = "0-12-174575-9",
keywords = "Multiresolution and Multilevel Analyses, Wavelet
Transforms, Spline-Wavelets, Other Mathematical Tools
for Time-Frequency Analysis, Wavelets and Fractals,
Numerical Methods and Algorithms, Applications",
abstract = "Wavelets: Theory, Algorithms, and Applications is the
fifth volume in the highly respected series, WAVELET
ANALYSIS AND ITS APPLICATIONS. This volume shows why
wavelet analysis has become a tool of choice in fields
ranging from image compression, to signal detection and
analysis in electrical engineering and geophysics, to
analysis of turbulent or intermittent processes. The 28
papers comprising this volume are organized into seven
subject areas: multiresolution analysis, wavelet
transforms, tools for time-frequency analysis, wavelets
and fractals, numerical methods and algorithms, and
applications. More than 135 figures supplement the
text.",
}
@Book{chu:tool,
title = "Wavelets: {A} Mathematical Tool for Signal Analysis",
author = "Charles K. Chui",
series = "SIAM Monographs on Mathematical Modeling and
Computation",
year = "1997",
publisher = SIAM,
address = "Philadelphia",
ISBN = "0-89871-384-6",
abstract = "Wavelets continue to be powerful mathematical tools
that can be used to solve problems for which the
Fourier (spectral) method does not perform well or
cannot handle. This book is for engineers, applied
mathematicians, and other scientists who want to learn
about using wavelets to analyze, process, and
synthesize images and signals. Applications are
described in detail and there are step-by-step
instructions about how to construct and apply wavelets.
The only mathematically rigorous monograph written by a
mathematician specifically for nonspecialists, it
describes the basic concepts of these mathematical
techniques, outlines the procedures for using them,
compares the performance of various approaches, and
provides information for problem solving, putting the
reader at the forefront of current research.",
}
@Book{chu:tutorial,
title = "Wavelets: {A} Tutorial in Theory and Applications",
author = "C. K. Chui",
volume = "2",
series = "Wavelet Analysis and its Applications",
year = "1992",
publisher = "Academic Press, Inc.",
ISBN = "0-12-174590-2",
abstract = "Wavelets: A Tutorial in Theory and Applications is the
second volume in the new series WAVELET ANALYSIS AND
ITS APPLICATIONS. As a companion to the first volume in
this series, this volume covers several of the most
important areas in wavelets, ranging from the
development of the basic theory such as construction
and analysis of wavelet bases to an introduction of
some of the key applictions, including Mallat's local
wavelet maxima technique in second generagion image
coding.",
}
@Proceedings{cia-cox-mon-pav:advanced,
title = "Advanced Mathematical Tools in Metrology",
booktitle = "Advanced Mathematical Tools in Metrology",
editor = "P. Ciarlini and M. Cox and R. Monaco and F. Pavese",
volume = "16",
series = "Advances in Mathematics for Applied Sciences",
publisher = "World Scientific",
address = "Singapore",
year = "1994",
URL = "http://www.wspc.co.uk/wspc/Books/book_series.html",
note = "Proceedings of the International Workshop",
}
@Article{cim-etal:time-series,
title = "Time series analysis of geological data",
author = "G. Cimino and G. Del Duce and L. K. Kadonaga and
G. Rotundo and A. Sisani and G. Stabile and
B. Tirozzi and M. Whiticar",
journal = CG,
volume = "161",
number = "1-3",
pages = "253--270",
year = "1999",
abstract = "",
}
@Article{cly-par-vid:multiple,
title = "Multiple shrinkage and subset selection in wavelets",
author = "Clyde, M. and Parmigiani, G. and Vidakovic, B.",
journal = BKA,
volume = "85",
number = "2",
pages = "391--401",
year = "1998",
keywords = "",
abstract = "This paper discusses Bayesian methods for multiple
shrinkage estimation in wavelets. Wavelets are used in
applications for data denoising, via shrinkage of the
coefficients towards zero, and for data compression, by
shrinkage and setting small coefficients to zero. We
approach wavelet shrinkage by using Bayesian
hierarchical models, assigning a positive prior
probability to the wavelet coefficients being zero. The
resulting estimator for the wavelet coefficients is a
multiple shrinkage estimator that exhibits a wide
variety of nonlinear patterns. We discuss fast
computational implementations, with a focus on
easy-to-compute analytic approximations as well as
importance sampling and Markov chain Monte Carlo
methods. Multiple shrinkage estimators prove to have
excellent mean squared error performance in
reconstructing standard test functions. We demonstrate
this in simulated test examples, comparing various
implementations of multiple shrinkage to commonly-used
shrinkage rules. Finally, we illustrate our approach
with an application to the so-called 'glint' data.",
}
@TechReport{cly-geo:empirical,
title = "Empirical Bayes Estimation in Wavelet Nonparametric
Regression",
author = "Merlise A. Clyde and Edward I. George",
number = "99--06",
institution = "Institute of Statistics and Decision Sciences, Duke
University",
year = "1999",
}
@Article{coh-dau-via:interval,
title = "Wavelets on the interval and fast wavelet transforms",
author = "A. Cohen and I. Daubechies and P. Vial",
journal = ACHA,
volume = "1",
number = "1",
year = "1993",
pages = "54--81",
keywords = "fast wavelet transform, orthonormal wavelet bases,
interval",
abstract = "The authors discuss several constructions of
orthonormal wavelet bases on the interval, and they
introduce a new construction that avoids some of the
disadvantages of earlier constructions.",
}
@Book{coh-rya:multiscale,
title = "Wavelets and Multiscale Signal Processing",
author = "A. Cohen and R. D. Ryan",
publisher = "Chapman \& Hall",
year = "1995",
pages = "248",
keywords = "Introduction. Multiresolution analysis. Introduction.
The continuous point of view. The discrete point of
view. The multivariate case. Conclusions. Wavelets and
conjugate quadrature filters. Introduction. The general
case. The finite case. Wavelets with compact support.
Action of the FWT on oscillating signals. The
regularity of scaling functions and wavelets.
Introduction. Regularity and oscillation. The
subdivision algorithms. Spectral estimates of the
regularity. Estimation of the Lp-Sobolev exponent.
Applications. Biorthogonal wavelet bases. Introduction.
General principles of Subband coding. Unconditional
biorthogonal wavelet bases. Dual filters and
biorthogonal Riesz bases. Examples and applications.
Stochastic processes. Introduction. Linear
approximation. Linear approximation of images.
Approximation and compression of real images. Piecewise
stationary processes. Nonlinear approximation.
Quasi-analytic wavelet bases. Multivariate
constructions. Multiscale unconditional bases.
Notation. References.",
abstract = "Since their appearance in the mid-1980s, wavelets and,
more generally, multiscale methods have become powerful
tools in mathematical analysis and in applications to
numerical analysis and signal processing. This book is
based on Ondelettes et Traitement Numerique du Signal
by Albert Cohen. It has been translated from French by
Robert D. Ryan and extensively updated by both Cohen
and Ryan. It studies the existing relations between
filter banks and wavelet decompositions and shows how
these relations can be exploited in the context of
digital signal processing. Throughout, the book
concentrates on the fundamentals. It begins with a
chapter on the concept of multiresolution analysis,
which contains complete proofs of the basic results.
The description of filter banks that are related to
wavelet bases is elaborated in both the orthogonal case
(Chapter 2), and in the biorthogonal case (Chapter 4).
The regularity of wavelets, how this is related to the
properties of the filters, and the importance of
regularity for the algorithms are the subjects of
Chapter 3. Chapter 5 looks at multiscale decomposition
as it applies to stochastic processing, in particular
to signal and image processing. Wavelets and Multiscale
Signal Processing will be of particular interest to
mathematicians working in analysis, academic and
research electrical engineers, and researchers who need
to analyse time series, in areas such as hydrodynamics,
aeronautics, meteorology, geophysics, statistics and
economics.",
}
@Article{coh-raz-mal:adaptive,
title = "Adaptive suppression of {W}igner interference-terms
using shift-invariant wavelet packet decompositions",
author = "Cohen, Israel and Raz, Shalom and Malah, David",
journal = SP,
volume = "73",
number = "3",
year = "1999",
pages = "203--223",
URL = "http://www.elsevier.nl/cas/tree/store/sigpro/1999/73/3/1340.pdf",
abstract = "The Wigner distribution (WD) possesses a number of
desirable mathematical properties relevant to
time-frequency analysis. However, the presence of
interference terms renders the WD of multicomponent
signals extremely difficult to interpret. In this
work, we propose adaptive suppression of
interference terms using the shift-invariant wavelet
packet decomposition. A prescribed signal is
expanded on its best basis and transformed into the
Wigner domain. Subsequently, the interference terms
are eliminated by adaptively thresholding the
cross-WD of interactive basis functions, according
to their amplitudes and distance in an idealized
time--frequency plane. We define a distance measure
that weighs the Euclidean distance with the local
distribution of the signal. The amplitude and
distance thresholds control the cross-term
interference, the useful properties of the
distribution, and the computational complexity. The
properties of the resultant modified Wigner
distribution (MWD) are investigated, and its
performance in eliminating interference terms, while
still retaining high-energy resolution, is compared
with that of other existing approaches. It is shown
that the proposed MWD is directly applicable to
resolving multicomponent signals. Each component is
determined as a partial sum of basis functions over
a certain equivalence class in the time--frequency
plane.",
}
@Article{coh-raz-mal:orthonormal,
title = "Orthonormal shift-invariant wavelet packet
decomposition and representation",
author = "Cohen, Israel and Raz, Shalom and Malah, David",
journal = SP,
volume = "57",
number = "3",
year = "1997",
pages = "251--270",
URL = "http://www-sipl.technion.ac.il/Sipl/siltd.ps",
keywords = "shift-invariant best basis time frequency wavelets
wavelet packets algorithm translation",
abstract = "In this work, a shifted wavelet packet (SWP)
library, containing all the time shifted wavelet
packet bases, is defined. A corresponding
shift-invariant wavelet packet decomposition (SIWPD)
search algorithm for a best basis' is
introduced. The search algorithm is representable by
a binary tree, in which a node symbolizes an
appropriate subspace of the original signal. We
prove that the resultant 'best basis' is orthonormal
and the associated expansion, characterized by the
lowest information cost, is shift- invariant. The
shift invariance stems from an additional degree of
freedom, generated at the decomposition stage and
incorporated into the search algorithm. The added
dimension is a relative shift between given parent
node and its respective children nodes. We prove
that for any subspace it suffices to consider one of
two alternative decompositions, made feasible by the
SWP library. These decompositions correspond to a
zero shift and a 2(-l) relative shift where l
denotes the resolution level. The optimal relative
shifts, which minimize the information cost, are
estimated using finite depth subtrees. By adjusting
their depth, the quadratic computational complexity
associated with SIWPD may be controlled at the
expense of the attained information cost down to
O(Nlog(2)N).",
}
@Article{coh-raz-mal:translation-invariant,
title = "Translation-invariant denoising using the minimum
description length criterion",
author = "Cohen, Israel and Raz, Shalom and Malah, David",
journal = SP,
volume = "75",
number = "3",
year = "1999",
pages = "201--223",
URL = "http://www.elsevier.nl/cas/tree/store/sigpro/sub/1999/75/3/1380.pdf",
keywords = "denoising signal estimation shift-invariant wavelet
packet minimum description length best basis
time-frequency representation Wigner distribution",
abstract = "A translation-invariant denoising method based on
the minimum description length (MDL) criterion and
tree-structured best-basis algorithms is
presented. A collection of signal models is
generated using an extended library of orthonormal
wavelet-packet bases, and an additive cost function,
approximately representing the MDL principle, is
derived. We show that the minimum description length
of the noisy observed data is achieved by utilizing
the shift-invarient wavelet packet decomposition
(SIWPD) and thresholding the resulting
coefficients. This approach is extendable to local
trigonometric decompositions, and corresponding
procedures to optimize either the library of bases
or the filter banks used at each node of the
expansion-tree are described. The signal estimator
is efficiently combined with a modified Wigner
distribution, yielding robust time-frequency
representations, characterized by high resolution
and suppressed interference-terms. The proposed
method is compared to alternative existing methods,
and its superiority is demonstrated by synthetic and
real data examples.",
}
@Book{coh:time-frequency,
title = "Time Frequency Analysis: Theory and Applications",
author = "Leon Cohen",
publisher = "Prentice Hall, Inc.",
address = "New Jersey",
year = "1994",
pages = "320",
keywords = "The Time and Frequency Description of Signals.
Instantaneous Frequency and the Complex Signal. The
Uncertainty Principle. Densities and Characteristic
Functions. The Need for Time-Frequency Analysis.
Time-Frequency Distributions: Fundamental Ideas. The
Short-Time Fourier Transform. The Wigner Distribution.
General Approach and the Kernel Method. Characteristic
Function Operator Method. Kernel Design for Reduced
Interference. Some Distributions. Further Developments.
Positive Distributions Satisfying the Marginals. The
Representation of Signals. Density of a Single
Variable. Joint Representations for Arbitrary
Variables. Scale. Joint Scale Representations",
abstract = "Featuring traditional coverage as well as new research
results that, until now, have been scattered throughout
the professional literature, this book brings together
--- in simple language --- the basic ideas and methods
that have been developed to study natural and man-made
signals whose frequency content changes with time;
e.g., speech, sonar and radar, optical images,
mechanical vibrations, acoustic signals,
biological/biomedical and geophysical signals. Covers
time analysis, frequency analysis, and scale analysis;
time-bandwidth relations; instantaneous frequency;
densities and local quantities; the short time Fourier
Transform; time-frequency analysis; the Wigner
representation; time-frequency representations;
computation methods; the synthesis problem;
spatial-spatial/frequency representations; time-scale
representations; operators; general joint
representations; stochastic signals; and higher order
time-frequency distributions. Illustrates each concept
with examples and shows how the methods have been
extended to other variables, such as scale.",
}
@InProceedings{coi-don:spinning,
title = "Time-Invariant Wavelet De-Noising",
author = "Ronald R. Coifman and David Donoho",
pages = "125--150",
URL = "ftp://playfair.stanford.edu/pub/donoho/TIDeNoise.ps.Z",
crossref = "ant-opp:wavelets",
abstract = "",
}
@InCollection{coi-etal:packets,
author = "Ronald R. Coifman and Yves Meyer and Stephen Quake
and Mladen Victor Wickerhauser",
title = "Signal Processing and Compression with Wavelet
Packets",
pages = "77--93",
crossref = "mey-roq:progress",
}
@InCollection{coi-mey-wic:analysis,
author = "Ronald R. Coifman and Yves Meyer and Mladen Victor
Wickerhauser",
title = "Wavelet analysis and signal processing",
pages = "153--178",
crossref = "rus-etal:wavelets",
URL = "ftp://wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/wasp.ps.Z.",
abstract = "This describes the use of wavelet analysis for various
tasks in signal processing.",
}
@InProceedings{coi-mey-wic:size,
title = "Size properties of wavelet packets",
author = "Ronald R. Coifman and Yves Meyer and Mladen Victor
Wickerhauser",
pages = "453--470",
crossref = "rus-etal:wavelets",
}
@Article{coi-wic:entropy-based,
title = "Entropy-Based Algorithms for Best Basis Selection",
author = "Ronald R. Coifman and Mladen Victor Wickerhauser",
journal = IEEETIT,
volume = "38",
number = "2",
year = "1992",
pages = "713--718",
URL = "http://wuarchive.wustl.edu/doc/techreports/wustl.edu/math/papers/entbb.ps.Z",
abstract = "Adapted waveform analysis uses a library of
orthonormal bases and an efficiency functional to match
a basis to a given signal or family of signals. It
permits efficient compression of a variety of signals,
such as sound and images. The predefined libraries of
modulated waveforms include orthogonal wavelet-packets
and localized trigonometric functions, and have
reasonably well-controlled time-frequency localization
properties. The idea is to build out of the library
functions an orthonormal basis relative to which the
given signal or collection of signals has the lowest
information cost. The method relies heavily on the
remarkable orthogonality properties of the new
libraries: all expansions in a given library conserve
energy and are thus comparable. Several cost
functionals are useful; one of the most attractive is
Shannon entropy, which has a geometric interpretation
in this context.",
}
@Article{cor-vet:time-varying,
title = "Orthogonal time-varying filter banks and wavelet
packets",
author = "Herley, C. and Vetterli, M.",
journal = IEEETSP,
volume = "42",
number = "10",
year = "1994",
pages = "2650--2663",
keywords = "orthogonal time-varying filter banks wavelet packets
construction time domain description two-channel
orthogonal filter bank one-sided signals
finite-length signals optimization subband tree
structures filter sets iteration continuous-time
bases half-line regions interval regions",
abstract = "We consider the construction of orthogonal
time-varying filter banks. By examining the time
domain description of the two- channel orthogonal
filter bank the authors find it possible to
construct a set of orthogonal boundary filters,
which allows to apply the filter bank to one-sided
or finite-length signals, without redundancy or
distortion. The method is constructive and
complete. There is a whole space of orthogonal
boundary solutions, and there is considerable
freedom for optimization. This may be used to
generate subband tree structures where the tree
varies over time, and to change between different
filter sets. The authors also show that the
iteration of discrete- time time-varying filter
banks gives continuous-time bases, just as in the
stationary case. This gives rise to wavelet, or
wavelet packet, bases for half-line and interval
regions.",
}
@Article{cor:boundary,
title = "Boundary filters for finite-length signals and
time-varying filter banks",
author = "Herley, C.",
journal = IEEETCS2,
volume = "42",
number = "2",
year = "1995",
pages = "102--114",
keywords = "finite-length signals time-varying filter banks
M-channel nonorthogonal case boundary filters
time-varying synthesis section nonorthogonal bases
frequency localization multirate filter banks",
abstract = "We examine the question of how to construct
time-varying filter banks in the most general
M-channel nonorthogonal case. We show that by
associating with both analysis and synthesis
operators a set of boundary filters, it is possible
to make the analysis structure vary arbitrarily in
time, and yet reconstruct the input with a similarly
time-varying synthesis section. There is no
redundancy or distortion introduced. This gives a
solution to the problem of applying filter banks to
finite length signals; it suffices to apply the
boundary filters at the beginning and end of the
signal segment. This also allows the construction of
orthogonal and nonorthogonal bases with essentially
any prescribed time and frequency localization, but
which, nonetheless, are based on structures with
efficient filter bank implementations.",
}
@Article{cou-cou:wavelet-HMMs,
title = "Wavelet-based method for nonparametric estimation of
{HMM}'s",
author = "Couvreur, L. and Couvreur, C.",
journal = IEEESPL,
volume = "7",
number = "2",
year = "2000",
pages = "25--27",
keywords = "",
abstract = "In this letter, we propose a new algorithm for
nonparametric estimation of hidden Markov models
(HMM's), The algorithm is based on a
``wavelet-shrinkage'' density estimator for the
state-conditional probability density functions of
the HMM's. It operates in an iterative fashion
similar to that of the EM reestimation formulae used
for maximum-likelihood estimation of parametric
HMM's. We apply the resulting algorithm to simple
examples and show its convergence. The proposed
method is also compared to classical nonparametric
HMM estimation based on quantization of observations
(``histograms'') and discrete HMM's.",
}
@Article{cra:xy,
title = "On the frequency function of $xy$",
author = "Cecil C. Craig",
journal = AofMS,
volume = "7",
pages = "1--15",
year = "1936",
}
@InProceedings{cre-hew:neighbor,
title = "A wavelet-based method of nearest neighbor pattern
classification using scale sequential matching",
author = "C. D. Creusere and G. Hewer",
booktitle = "Conference Record of the Twenty-Eighth Asilomar
Conference on Signals, Systems and Computers",
volume = "2",
editor = "A. Singh",
year = "1994",
pages = "1123--1127",
keywords = "nearest neighbor pattern classification, scale
sequential matching. wavelet-based method.
post-detection radar pulses, feature extraction.
trained nearest neighbor codebook. pattern classifier,
radar pulse fingerprinting. noise, Monte Carlo
simulations, shift invariant classifier, undecimated
wavelet transform, pulse edge, wavelet coefficients",
abstract = "In this method of pattern classification a wavelet
transform is used to extract features from the input
signal which are then compared in a scale sequential
manner (from coarse to fine) to a trained nearest
neighbor codebook. At each scale, possible
classification categories are eliminated until only one
class is left. We apply this pattern classifier to the
problem of fingerprinting post-detection radar pulses
and analyze its performance in noise using Monte Carlo
simulations. To make our classifier shift invariant, we
process the input with an undecimated wavelet transform
until the pulse edge is sensed and then start
decimating the wavelet coefficients as appropriate to
each scale.",
}
@Unpublished{cro-bar:fast-exact,
title = "Fast, Exact Synthesis of {G}aussian and
non{G}aussian Long-Range Dependent Processes",
author = "Matthew S. Crouse and Richard G. Baraniuk",
year = "1999",
note = "submitted to {\em IEEE Trans. on Info. Theory}",
URL = "http://www-dsp.rice.edu/publications/pub/fftMC.ps.Z",
abstract = "Wavelet-based statistical signal processing
techniques such as denoising and detection typically
model the wavelet coefficients as independent or
jointly Gaussian. These models are unrealistic for
many real-world signals. In this paper, we develop a
new framework for statistical signal processing
based on wavelet-domain hidden Markov models
(HMMs). The framework enables us to concisely model
the statistical dependencies and nonGaussian
statistics encountered with real-world
signals. Wavelet-domain HMMs are designed with the
intrinsic properties of the wavelet transform in
mind and provide powerful yet tractable
probabilistic signal models. Efficient Expectation
Maximization algorithms are developed for fitting
the HMMs to observational signal data. The new
framework is suitable for a wide range of
applications, including signal estimation,
detection, classification, prediction, and even
synthesis. To demonstrate the utility of
wavelet-domain HMMs, we develop novel algorithms for
signal denoising, classification, and detection.",
}
@Article{cro-now-bar:hidden,
title = "Wavelet-Based Statistical Signal Processing Using
Hidden Markov Models",
author = "Matthew S. Crouse and Robert D. Nowak and Richard
G. Baraniuk",
journal = IEEETSP,
volume = "46",
number = "4",
year = "1998",
URL = "http://www-dsp.rice.edu/publications/pub/wmarkov.ps.Z",
keywords = "",
abstract = "Wavelet-based statistical signal processing
techniques such as denoising and detection typically
model the wavelet coefficients as independent or
jointly Gaussian. These models are unrealistic for
many real-world signals. In this paper, we develop a
new framework for statistical signal processing
based on wavelet-domain hidden Markov models
(HMMs). The framework enables us to concisely model
the statistical dependencies and nonGaussian
statistics encountered with real-world
signals. Wavelet-domain HMMs are designed with the
intrinsic properties of the wavelet transform in
mind and provide powerful yet tractable
probabilistic signal models. Efficient Expectation
Maximization algorithms are developed for fitting
the HMMs to observational signal data. The new
framework is suitable for a wide range of
applications, including signal estimation,
detection, classification, prediction, and even
synthesis. To demonstrate the utility of
wavelet-domain HMMs, we develop novel algorithms for
signal denoising, classification, and detection.",
}
@Unpublished{dah-neu:locally,
title = "Locally Adaptive...",
author = "Rainer Dahlhaus and Michael H. Neumann",
year = "1999",
note = "StatLab Heidelberg, Institut f{\"u}r Angewandte
Mathematik",
URL = "ftp://statlab.uni-heidelberg.de/pub/reports/by.series/beitrag.60.ps",
abstract = "We fit a class of semiparametric models to a
nonstationary process. This class is parametrized by
a mean function \mu(.) and a p-dimensional function
theta(.) = (theta^{(1)}(.), ..., theta^{(p)}(.))'
that parametrizes the time-varying spectral density
f_{theta(.)}(\lambda). Whereas the mean function is
estimated by a usual kernel estimator, each
component of theta(.) is estimated by a nonlinear
wavelet method. According to a truncated wavelet
series expansion of theta^{(i)}(.), we define
empirical versions of the corresponding wavelet
coefficients by minimizing an empirical version of
the Kullback-Leibler distance. In the main smoothing
step, we perform nonlinear thresholding on these
coefficients, which finally provides a locally
adaptive estimator of theta^{(i)}(.). This method is
fully automatic and adapts to different smoothness
classes. It is shown that usual rates of convergence
in Besov smoothness classes are attained up to a
logarithmic factor.",
}
@Article{dah-new-von:nonlinear,
title = "Nonlinear wavelet estimation of time-varying
autoregressive processes",
author = "Rainer Dahlhaus and Michael H. Neumann and Rainer
{von Sachs}",
journal = "Bernoulli",
volume = "5",
number = "5",
year = "1999",
URL = "ftp://statlab.uni-heidelberg.de/pub/reports/by.series/report.09.ps",
abstract = "We consider nonparametric estimation of the
parameter functions a(i)(.), i = 1, ..., p, of a
time-varying autoregressive process. Choosing an
orthonormal wavelet basis representation of the
Functions a(i), the empirical wavelet coefficients
are derived from the time series data as the
solution of a least-squares minimization problem. In
order to allow the a(i) to be functions of
inhomogeneous regularity, we apply nonlinear
thresholding to the empirical coefficients and
obtain locally smoothed estimates of the a(i). We
show that the resulting estimators attain the usual
minimax L-2 rates up to a logarithmic factor,
simultaneously in a large scale of Besov
classes. The finite-sample behaviour of our
procedure is demonstrated by application to two
typical simulated examples."
}
@Article{dao-fra-wil:MAR,
title = "Multiscale autoregressive models and wavelets",
author = "Khalid Daoudi and Austin B. Frakt and Alan
S. Willsky",
journal = IEEETIT,
volume = "45",
number = "3",
year = "1999",
pages = "828--845",
}
@Article{dat-hir:wavelet-based,
title = "Wavelet-based estimations in fractional {B}rownian
motion",
author = "{D'Attellis}, C. E. and Hirchoren, G. A.",
journal = "Latin American Applied Research",
volume = "29",
number = "3-4",
year = "1999",
pages = "221--225",
abstract = "Fractional Brownian motion (fBm) is used as a model
of 1/f-type stochastic processes, an important class
of processes that characterize a large number of
physical phenomena. Since the Hurst parameter H
characterizes these processes, its estimation from a
signal is an important issue in many
applications. This paper points out some
applications of recent results on estimations of
fBm, and shows a new method for estimating the Hurst
parameter. Since variation in H indicates changes in
the physical system that produces the measured
signal, the determination of these variations is
relevant for failure detection. In this paper an
algorithm that allows the estimation of changes in
the Hurst parameter is introduced. The method is
based on multiresolution analysis. The results
obtained processing an acoustic emission signal from
a coating breakdown are presented.",
}
@Article{dau-lag:difference1,
title = "Two-scale difference equations, {I}",
author = "Ingrid Daubechies and J. Lagarias",
journal = SIAMJMA,
volume = "22",
year = "1991",
pages = "1388--1410",
}
@Article{dau-lag:difference2,
title = "Two-scale difference equations. {II}. {L}ocal
regularity, infinite products of matrices and
fractals",
author = "Ingrid Daubechies and J. Lagarias",
journal = SIAMJMA,
volume = "23",
year = "1992",
pages = "1031--1079",
abstract = "We study solutions of the functional equation
$f(x)=\sum\sp N\sb {n=0}c\sb nf(kx-n)$, where $k\geq 2$
is an integer, and $\sum\sp N\sb {n=0}c\sb n=k$. Part I
showed [SIAM J. Math. Anal. 22 (1991), no. 5,
1388--1410; MR 92d:39001] that equations of this type
have at most one $L\sp 1$-solution up to a
multiplicative constant, which necessarily has compact
support in $[0,N/k-1]$. This paper gives a time-domain
representation for such a function $f(x)$ (if it
exists) in terms of infinite products of matrices (that
vary as $x$ varies). Sufficient conditions are given on
$\{c\sb n\}$ for a continuous nonzero $L\sp 1$-solution
to exist. Additional conditions sufficient to guarantee
$f\in C\sp r$ are also given. The infinite matrix
product representations are used to bound from below
the degree of regularity of such an $L\sp 1$-solution
and to estimate the Holder exponent of continuity of
the highest-order well-defined derivative of $f(x)$.
Such solutions $f(x)$ are often smoother at some points
than others. For certain $f(x)$ a hierarchy of fractal
sets in $\bold R$ corresponding to different Holder
exponents of continuity for $f(x)$ is described.",
}
@TechReport{dau-swe:factor,
author = "I. Daubechies and W. Sweldens",
title = "Factoring Wavelet Transforms into Lifting Steps",
institution = "Bell Laboratories, Lucent Technologies",
year = "1996",
URL = "http://cm.bell-labs.com/who/wim/papers/factor.ps.gz",
abstract = "The lifting scheme is a new flexible tool for
constructing wavelets and wavelet transforms. In this
paper, we use the Euclidean algorithm to show how any
discrete wavelet transform or two band subband
transform with finite filters can be obtained with a
finite number of lifting steps starting from the Lazy
wavelet (or polyphase transform). We show a bound on
the number of lifting steps which is proportional to
the length of the filters. This factorization provides
an alternative for the lattice factorization, with the
advantage that it can also be used in the biorthogonal
(non-unitary) case. The lifting factorization
asymptotically reduces the computational complexity of
the transform by a factor of two and allows for wavelet
transforms that map integers to integers.",
}
@InCollection{dau:connection,
title = "Orthonormal Bases of Wavelets with Finite Support --
Connection with Discrete Filters",
author = "Ingrid Daubechies",
pages = "38--66",
crossref = "com-gro-tch:wavelets",
abstract = "",
}
@Article{dau:orthonormal,
title = "Orthonormal bases of compactly supported wavelets",
author = "Ingrid Daubechies",
journal = "Communications in Pure and Applied Mathematics",
volume = "41",
pages = "909--996",
year = "1988",
}
@Book{dau:ten,
title = "Ten Lectures on Wavelets",
author = "Ingrid Daubechies",
series = "CBMS-NSF Regional Conference Series in Applied
Mathematics",
volume = "61",
publisher = SIAM,
address = "Philadelphia",
year = "1992",
URL = "http://www.siam.org/catalog/mcc02/daubechi.htm",
keywords = "Introduction; Preliminaries and Notation; The What,
Why, and How of Wavelets; The Continuous Wavelet
Transform; Discrete Wavelet Transforms: Frames;
Time-Frequency Density and Orthonormal Bases;
Orthonormal Bases of Wavelets and Multiresolutional
Analysis; Orthonormal Bases of Compactly Supported
Wavelets; More About the Regularity of Compactly
Supported Wavelets; Symmetry for Compactly Supported
Wavelet Bases; Characterization of Functional Spaces by
Means of Wavelets; Generalizations and Tricks for
Orthonormal Wavelet Bases; References; Indexes.",
abstract = "Wavelets are a mathematical development that may
revolutionize the world of information storage and
retrieval according to many experts. They are a fairly
simple mathematical tool now being applied to the
compression of data--such as fingerprints, weather
satellite photographs, and medical x-rays--that were
previously thought to be impossible to condense without
losing crucial details. This monograph contains 10
lectures presented by Dr. Daubechies as the principal
speaker at the 1990 CBMS-NSF Conference on Wavelets and
Applications. The author has worked on several aspects
of the wavelet transform and has developed a collection
of wavelets that are remarkably efficient. The opening
chapter provides an overview of the main problems
presented in the book. Following chapters discuss the
theoretical and practical aspects of wavelet theory,
including wavelet transforms, orthonormal bases of
wavelets, and characterization of functional spaces by
means of wavelets. The last chapter presents several
topics under active research, as multidimensional
wavelets, wavelet packet bases, and a construction of
wavelets tailored to decompose functions defined in a
finite interval. Because of their interdisciplinary
origins, wavelets appeal to scientists and engineers of
many different backgrounds.",
}
@Article{dau:time-frequency,
title = "The Wavelet Transform, Time-Frequency Localization and
Signal Analysis",
author = "I. Daubechies",
journal = IEEETIT,
volume = "36",
number = "5",
year = "1990",
pages = "961--1005",
abstract = "Two different procedures for effecting a frequency
analysis of a time-dependent signal locally in time are
studied. The first procedure is the short-time or
windowed Fourier transform; the second is the wavelet
transform, in which high-frequency components are
studied with sharper time resolution than low-frequency
components. The similarities and the differences
between these two methods are discussed. For both
schemes a detailed study is made of the reconstruction
method and its stability as a function of the chosen
time-frequency density. Finally, the notion of
time-frequency localization is made precise, within
this framework, by two localization theorems.",
}
@InCollection{dau:wavelet-transform,
title = "The Wavelet Transform: {A} Method for Time-Frequency
Localization",
author = "Ingrid Daubechies",
pages = "366--417",
crossref = "hay:advances",
keywords = "",
abstract = "",
}
@Article{dav-lab-les:commodity,
title = "Wavelet Analysis of Commodity Price Behavior",
author = "Russel Davidson and Walter C. Labys and
Jean-Baptiste Lesourd",
journal = CE,
volume = "11",
number = "",
year = "1998",
pages = "103--128",
}
@InCollection{dav-mar-wis:multifractal,
title = "Wavelet-based multifractal analysis of non-stationary
and/or intermittent geophysical signals",
author = "Anthony Davis and Alexander Marshak and Warren
Wiscombe",
pages = "249--298",
crossref = "fou-kum:geophysics",
URL = "ftp://climate.gsfc.nasa.gov/pub/davis/Wavelets/Wavelets.text.PS.Z",
abstract = "",
}
@Article{dav:distribution,
title = "The Distribution of a Linear Combination of $\chi^2$
Random Variables",
author = "Robert B. Davies",
journal = AS,
volume = "29",
number = "",
year = "1980",
pages = "323--333",
keywords = "Quadratic form",
}
@InCollection{dav:tables,
title = "Tables of the Correlation Coefficient",
author = "F. N. David",
booktitle = "Biometrika Tables for Statisticians",
editor = "E. S. Pearson and H. O. Hartley",
publisher = "Cambridge University Press",
address = "Cambridge",
volume = "1",
edition = "3",
year = "1966",
}
@Article{del-gam-sal:interannual,
title = "Interannual signals in length of day and atmospheric
angular momentum",
author = "{del Rio}, R. A and Gambis, D. and Salstein, D. A.",
journal = AG,
volume = "18",
number = "3",
year = "2000",
pages = "347--364",
keywords = "Meteorology and atmospheric dynamics (general
circulation) - Solar physics, astrophysics and
astronomy (celestial mechanics)",
abstract = "Atmospheric angular momentum (AAM) and length of day
(LOD) series are investigated for their
characteristics on interannual time scales during
the half-century period 1949 to 1998. During this
epoch, the interannual variability in LOD can be
separated naturally into three bands: a
quasi-biennial, a triennial-quadrennial and one at
six-seven years. The atmosphere appears to excite
the first two bands, while it does not contribute to
the last. Considering the quasi-biennial (QB) band
alone, the atmosphere appears to excite most of its
signal in LOD, but it arises from separate
fluctuations with stratospheric and tropospheric
origin. Thus, although close in frequency,
stratospheric and tropospheric processes differ in
their amplitude and phase variability. The time
shift can be noted especially during the strong El
Nino events of 1982-83 and 1997-98
when both processes have positive phase and thus
combine to help produce particularly strong peak in
AAM and LOD. In addition, we have reconfirmed the
downward propagation in the stratosphere and upward
propagation in the troposphere of AAM observed in
earlier studies for other variables. In the
triennial-quadrennial (TQ) band, time-variable
spectral analyses reveal that LOD and AAM contain
strong variability, with periods shorter than four
years before 1975 and longer thereafter. This signal
originates mainly within the troposphere and
propagates upwards from the lower to the higher
layers of the troposphere. According to a zonal
analysis, an equatorial poleward mode, strongly
linked to the SOI, explains more than 60% of the
total variability at these ranges. In addition, this
study also indicates that an equatorward mode,
originating within polar latitudes, explains, on
average, more than 15% of the triennial-quadrennial
oscillation (TQO) variability in AAM, and up to 30%
at certain epochs. Finally, a six year period in LOD
noted in earlier studies, as well as in lengthier
series covering much of the century, is found to be
absent in atmospheric excitations, and it is thus
likely to arise from mantle/core interactions.",
}
@Article{del-jud:computation,
journal = JAT,
volume = "88",
number = "1",
year = "1997",
pages = "47--79",
title = "{O}n the computation of wavelet coefficients",
author = "B. Delyon and A. Juditsky",
URL = "http://www.irisa.fr/EXTERNE/bibli/pi/pi856.html",
abstract = "We consider fast algorithms of wavelet decomposition
of a function f when discrete observations of f (supp f
subset of or equal to[0,1](d)) are available. The
properties of the algorithms are studied for three
types of observation design which for $d=1$ can be
described as follows: the regular design, when the
observations $f(xi)$ are taken on the regular grid
$x(i)=i/N$, $i=1, ..., N$; the case of a jittered
regular grid, when it is only known that for all 1 less
than or equal to i less than or equal to $N$, $i/N$
less than or equal to $x(i)<i+1)/N$; and the random
design case; in which $x(i), i=1, ..., N$, are
independent and identically distributed random
variables on [0,1]. We show that these algorithms are
in a certain sense efficient when the accuracy of the
approximation is concerned. The proposed algorithms are
computationally straightforward; the whole effort to
compute the decomposition is order $N$ for the sample
size $N$.",
}
@InCollection{del-jud:estimation,
title = "Estimating Wavelet Coefficients",
author = "Bernard Delyon and Anatoli Juditsky",
pages = "151--168",
crossref = "ant-opp:wavelets",
URL = "",
email = "iouditsk@irisa.fr",
abstract = "",
}
@Article{del-wei:M-band,
title = "{\em M}-band wavepacket-based transient signal
detector using a translation-invariant wavelet
transform",
author = "Stephen del Marco and John Weiss",
journal = OE,
volume = "33",
number = "7",
year = "1994",
pages = "2175--2182",
abstract = "This paper develops a two-dimensional M-band
translation-invariant wavelet transform (2-D MTI). Use
of the MTI overcomes the shift-variance of the wavelet
transform by applying a cost function over M shifts of
the input signal. The new transform is proven to be
translation-invariant. Use of M-band wavelets enables a
finer frequency partitioning and greater energy
compaction in the transform representation. Examples
are presented which show that the translation-invariant
transforms provide superior energy concentration
compared to the corresponding nominal wavelet
transforms. Examples are also presented comparing the
energy concentration capability of M-band wavelets and
the modulated lapped transform (MLT). We explored the
MTI as a tool for image processing by using it to
represent several different images.",
}
@Article{del-wei:improved,
title = "Improved transient signal detection using a
wavepacket-based detector with an extended
translation-invariant wavelet transform",
author = "Stephen del Marco and John Weiss",
journal = IEEETSP,
volume = "45",
number = "4",
year = "1997",
pages = "841--850",
URL = "http://www.tiac.net/users/nurit/ETI/ETI.html",
abstract = "This paper presents the theory of M-band, extended
translation-invariant (ETI) wavelet transforms. The ETI
generalizes the translation-invariant wavelet transform
of Weiss. It is shown that iteration of the ETI, in a
tree structure, provides a signal decomposition into an
orthonormal wavepacket basis, Other properties such as
translation invariance and invertibility of the
transform are proven, The theory is then applied to
transient signal detection through development of a
family of translation-invariant wavepacket-based
detectors. This family of detectors provides improved
performance over previously defined wavepacket-based
detectors, A performance analysis is conducted. ROC
curves generated by Monte-Carlo simulation are
presented, indicating detector performance, Detector
performance is demonstrated to be independent of the
signal translation.",
keywords = "compactly supported wavelets, representation,
algorithms",
}
@TechReport{der-lou-war:arbitrary,
title = "Multiresolution Analysis for Sufaces of Arbitrary
Topological Type",
author = "Tony D. DeRose and Michael Lounsbery and Joe Warren",
institution = "Department of Computer Science and Engineering,
University of Washington",
number = "93-10-05",
year = "1993",
}
@Article{dij-maz-bag:reciprocal,
title = "Reciprocal processes on a tree-modeling and estimation
issues",
author = "R. W. Dijkerman and R. R. Mazumdar and A. Bagchi",
journal = IEEETAC,
volume = "40",
number = "2",
year = "1995",
pages = "330--335",
keywords = "reciprocal processes, estimation issues,
multiresolution decomposition methods, discrete wavelet
transformation, truncated N-ary trees, nearest neighbor
models, recursive description, autoregressive
processes, zero-valued boundary values, smoothing
equations",
abstract = "Motivated by multiresolution decomposition methods
such as the discrete wavelet transformation, the
authors introduce reciprocal processes on truncated
N-ary trees. The authors discuss the relationship
between such processes and nearest neighbor models. The
authors show that they can derive a recursive
description of the process, and that all reciprocal
processes on N-ary trees reduce to autoregressive
processes in the case of zero-valued boundary values at
the bottom of the tree, corresponding to truncation of
the tree. The authors then study the smoothing
equations associated with such models.",
}
@Article{dij-maz:correlation,
title = "On the correlation structure of the wavelet
coefficients of fractional {B}rownian motion",
author = "R. W. Dijkerman and R. R. Mazumdar",
journal = IEEETIT,
volume = "40",
number = "5",
year = "1994",
pages = "1609--1612",
keywords = "correlation structure, wavelet coefficients,
fractional Brownian motion, normalized correlation,
decay",
abstract = "Shows that the interdependence of the discrete wavelet
coefficients of fractional Brownian motion, defined by
normalized correlation, decays exponentially fast
across scales and hyperbolically fast along time.",
}
@Article{dij-maz:representation,
title = "Wavelet representations of stochastic processes and
multiresolution stochastic models",
author = "R. W. Dijkerman and R. R. Mazumdar",
journal = IEEETSP,
volume = "42",
number = "7",
year = "1994",
pages = "1640--1652",
keywords = "stochastic processes, multiresolution stochastic
models, deterministic signal analysis, wavelet
representations, wavelet bases, time domain,
correlation structure, discrete wavelet coefficients,
correlation decay, trees, time process, approximations,
wavelet transform, decorrelation",
abstract = "Deterministic signal analysis in a multiresolution
framework through the use of wavelets has been
extensively studied very successfully in recent years.
In the context of stochastic processes, the use of
wavelet bases has not yet been fully investigated. We
use compactly supported wavelets to obtain
multiresolution representations of stochastic processes
with paths in L/sup 2/ defined in the time domain. We
derive the correlation structure of the discrete
wavelet coefficients of a stochastic process and give
new results on how and when to obtain strong decay in
correlation along time as well as across scales. We
study the relation between the wavelet representation
of a stochastic process and multiresolution stochastic
models on trees proposed by Basseville et al. (see IEEE
Trans. Inform. Theory, vol.38, p.766-784, Mar. 1992).
We propose multiresolution stochastic models of the
discrete wavelet coefficients as approximations to the
original time process. These models are simple due to
the strong decorrelation of the wavelet transform.
Experiments show that these models significantly
improve the approximation in comparison with the often
used assumption that the wavelet coefficients are
completely uncorrelated.",
}
@Article{don-joh-ker-pic:asymptopia,
title = "Wavelet Shrinkage: Asymptopia? (with discussion)",
author = "David L. Donoho and Iain M. Johnstone and G{\'e}rard
Kerkyacharian and Dominique Picard",
journal = JRSSB,
volume = "57",
number = "2",
year = "1995",
pages = "301--369",
URL = "http://playfair.Stanford.EDU/reports/donoho/asymp.ps.Z",
abstract = "Much recent effort has sought asymptotically minimax
methods for recovering infinite dimensional objects -
curves, densities, spectral densities, images - from
noisy data. A now rich and complex body of work
develops nearly or exactly minimax estimators for an
array of interesting problems. Unfortunately, the
results have rarely moved into practice, for a variety
of reasons - among them being similarity to known
methods, computational intractability and lack of
spatial adaptivity. We discuss a method for curve
estimation based on n noisy data: translate the
empirical wavelet coefficients towards the origin by an
amount [sq.root](2 log n) [sigma]/[sq.root]n. The
proposal differs from those in current use, is
computationally practical and is spatially adaptive; it
thus avoids several of the previous objections.
Further, the method is nearly minimax both for a wide
variety of loss functions - pointwise error, global
error measured in Lp-norms, pointwise and global errors
in estimation of derivatives - and for a wide range of
smoothness classes, including standard Hölder and
Sobolev classes, and bounded variation. This is a much
broader near optimality than anything previously
proposed: we draw loose parallels with near optimality
in robustness and also with the broad near
eigenfunction properties of wavelets themselves.
Finally, the theory underlying the method is
interesting, as it exploits a correspondence between
statistical questions and questions of optimal recovery
and information-based complexity.",
keywords = "Adaptive estimation Besov spaces Density estimation
Minimax estimation Nonparametric regression Optimal
recovery Spatial adaptation Wavelet orthonormal bases",
}
@Article{don-joh:adapting,
title = "Adapting to unknown smoothness by wavelet shrinkage",
author = "David L. Donoho and Iain M. Johnstone",
journal = JASA,
volume = "90",
number = "",
year = "1995",
pages = "1200--1224",
URL = "http://playfair.Stanford.EDU/reports/donoho/isaws.ps.Z",
}
@Article{don-joh:asymptotic,
title = "Asymptotic minimaxity of wavelet estimators with
sampled data",
author = "David L. Donoho and Iain M. Johnstone",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "1--32",
keywords = "Besov spaces bounded operators between Besov spaces
Minimax estimation thresholding wavelet transforms
of sampled data wavelets white noise equivalence",
abstract = "Donoho and Johnstone (1998) studied a setting where
data were obtained in the continuum white noise
model and shop;ed that scalar nonlinearities applied
to wavelet coefficients gave estimators which were
asymptotically minimax over Besov balls. They
claimed that this implied similar asymptotic
minimaxity results in the sampled-data model. In
this paper we carefully develop and fully prove this
implication. Our results are based on a careful
definition of an empirical wavelet transform and
precise bounds on the discrepancy between empirical
wavelet coefficients and the theoretical wavelet
coefficients.",
}
@Article{don-joh:ideal,
title = "Ideal spatial adaptation by wavelet shrinkage",
author = "David L. Donoho and Iain M. Johnstone",
journal = BKA,
volume = "81",
number = "3",
year = "1994",
pages = "425--455",
URL = "http://playfair.Stanford.EDU/reports/donoho/ausws.ps.Z",
}
@Article{don-joh:minimax,
title = "Minimax estimation via wavelet shrinkage",
author = "David L. Donoho and Iain M. Johnstone",
journal = AofS,
volume = "26",
number = "3",
year = "1998",
pages = "879--921",
URL = "http://playfair.Stanford.EDU/reports/donoho/mews.ps.Z",
keywords = "minimax decision theory minimax Bayes estimation
Besov Holder Sobolev Triebel spaces nonlinear
estimation white noise model nonparametric
regression orthonormal bases of compactly supported
wavelets renormalization white noise approximation",
abstract = "We attempt to recover an unknown function from
noisy, sampled data. Using orthonormal bases of
compactly supported wavelets, we develop a nonlinear
method which works in the wavelet domain by simple
nonlinear shrinkage of the empirical wavelet
coefficient. The shrinkage can be tuned to be nearly
minimax over any member of a wide range of Triebel-
and Besov-type smoothness constraints and
asymptotically minimax over Besov bodies with p less
than or equal to q. Linear estimates cannot achieve
even the minimax rates over Triebel and Besov
classes with p < 2, so the method can significantly
outperform every linear method (e.g., kernel,
smoothing spline, sieve) in a minimax
sense. Variants of our method based on simple
threshold nonlinear estimators are nearly
minimax. Our method possesses the interpretation of
spatial adaptivity; it reconstructs using a kernel
which may vary in shape and bandwidth from point to
point, depending on the data. Least favorable
distributions for certain of the Triebel and Besov
scales generate objects with sparse wavelet
transforms. Many real objects have similarly sparse
transforms, which suggests that these minimax
results are relevant for practical problems. Sequels
to this paper, which was first drafted in November
1990, discuss practical implementation, spatial
adaptation properties, universal near minimaxity and
applications to inverse problems.",
}
@Article{don-joh:neo-classical,
title = "Neo-classical minimax problems, thresholding and
adaptive function estimation",
author = "David L. Donoho and Iain M. Johnstone",
journal = Ber,
volume = "2",
number = "1",
year = "1996",
pages = "39--62",
URL = "",
abstract = "We study the problem of estimating θ from data
Y&126;N(θ, σ2) under squared-error loss. We
define three new scalar minimax problems in which the
risk is weighted by the size of θ. Simple
thresholding gives asymptotically minimax estimates in
all three problems. We indicate the relationships of
the new problems to each other and to two other
neo-classical problems: the problems of the bounded
normal mean and of the risk-constrained normal mean.
Via the wavelet transform, these results have
implications for adaptive function estimation in two
settings: estimating functions of unknown type and
degree of smoothness in a global l2 norm; and
estimating a function of unknown degree of local Hölder
smoothness at a fixed point. In the latter setting, the
scalar minimax results imply: Lepskii's results that it
is not possible fully toadapt the unknown degree of
smoothness without incurring a performance cost; and
that simple thresholding of the empirical wavelet
transform gives an estimate of a function at a fixed
point which is, to within constants, optimally adaptive
to unknown degree of smoothness.",
keywords = "adaptive estimation; lp balls; minimax estimation;
weak lp balls",
}
@Unpublished{don-mal-von:covariances,
title = "Estimating Covariances of Locally Stationary
Processes: Rates of Convergence of Best Basis Methods",
author = "David L. Donoho and Steph{\'a}ne Mallat and Rainer
{von Sachs}",
year = "1997",
note = "Unpublished",
}
@TechReport{don:interpolating,
title = "Interpolating Wavelet Transforms",
author = "David L. Donoho",
year = "1992",
institution = "Technical Report 408, Department of Statistics,
Stanford University",
URL = "http://playfair.Stanford.EDU/reports/donoho/interpol.ps.Z",
}
@InProceedings{don:nonlinear,
title = "Nonlinear Wavelet Methods for Recovery of Signals,
Densities, and Spectra from Indirect and Noisy Data",
author = "David L. Donoho",
booktitle = "Proceedings of Symposia in Applied Mathematics",
organization = AMS,
volume = "47",
year = "1993",
pages = "173--205",
URL = "http://playfair.Stanford.EDU/reports/donoho/ShortCourseFigs.epsf.shar.Z",
abstract = "Wavelet methods for the recovery of objects from noisy
and incomplete data are described. The common themes:
(a) the new methods use nonlinear operations in the
wavelet domain; (b) they accomplish tasks which are not
possible by traditional linear/Fourier approaches to
such problems. An attempt is made to indicate the
heuristic principles, theoretical foundations and
possible application areas for these methods, i.e.
wavelet de-noising, wavelet approaches to linear
inverse problems, wavelet packet de-noising, segmented
multiresolutions, and nonlinear multi-resolutions.",
}
@InCollection{don:smooth,
author = "David L. Donoho",
title = "Smooth Wavelet Decompositions with Blocky Coefficient
Kernels",
pages = "1--43",
URL = "http://playfair.Stanford.EDU/reports/donoho/blocky.ps.Z",
crossref = "sch-web:recent",
abstract = "",
}
@Article{don:soft,
title = "De-noising by Soft-Thresholding",
author = "David L. Donoho",
journal = IEEETIT,
volume = "41",
number = "3",
year = "1995",
pages = "613--627",
URL = "http://playfair.Stanford.EDU/reports/donoho/denoiserelease3.ps.Z",
keywords = "soft-thresholding, de-noising, reconstruction, unknown
function, noisy data, standard Gaussian random
variables, wavelet domain, empirical wavelet
coefficients, estimator, probability, smoothness
measures, statistical inference, optimal recovery
model",
abstract = "Donoho and Johnstone (1994) proposed a method for
reconstructing an unknown function f on (0,1) from
noisy data d/sub i/=f(t/sub i/)+ sigma z/sub i/, i=0,
..., n-1,t/sub i/=i/n, where the z/sub i/ are
independent and identically distributed standard
Gaussian random variables. The reconstruction f*/sub n/
is defined in the wavelet domain by translating all the
empirical wavelet coefficients of d toward 0 by an
amount sigma . square root (2log (n)/n). The authors
prove two results about this type of estimator.
(Smooth): with high probability f*/sub n/ is at least
as smooth as f, in any of a wide variety of smoothness
measures. (Adapt): the estimator comes nearly as close
in mean square to f as any measurable estimator can
come, uniformly over balls in each of two broad scales
of smoothness classes. These two properties are
unprecedented in several ways. The present proof of
these results develops new facts about abstract
statistical inference and its connection with an
optimal recovery model.",
}
@Article{dor:least-asymmetric,
title = "On the least asymmetric wavelets",
author = "Doroslova\v{c}ki, Milo\v{s} L.",
journal = IEEETSP,
volume = "46",
number = "4",
year = "1998",
pages = "1125-1130",
keywords = "least asymmetric wavelets scaling functions second
moment wavelet-generating discrete-time filter uncertainty
relation discrete-time signals asymmetry measures signal
processing transfer function phase nonlinearities
minimisation",
abstract = "The asymmetry of Daubechies' (1988, 1992) scaling
functions and wavelets can be diminished by minimizing a
special second moment in time for the wavelet-generating
discrete-time filter. The moment is involved in an
uncertainty relation for discrete-time signals. Other
measures of asymmetry are addressed as well, and
corresponding results are compared.",
}
@Article{dow-sil:multiple,
title = "The discrete multiple wavelet transform and
thresholding methods",
author = "T. R. Downie and B. W. Silverman",
journal = IEEETSP,
volume = "46",
number = "9",
year = "1998",
pages = "2558--2562",
URL = "http://www.stats.bris.ac.uk/~bernard/threshmwave3.ps.gz",
keywords = "",
abstract = "",
}
@Article{dro-kat:new,
title = "New filter banks and more regular wavelets",
author = "Karim Drouiche and Djalil Kateb",
journal = IEEETSP,
volume = "47",
number = "8",
year = "1999",
pages = "2220--2227",
URL = "",
keywords = "",
abstract = "",
}
@Article{duf-mil:prior,
title = "Statistical signal restoration with $1/f$ wavelet
domain prior models",
author = "R. M. Dufour and E. L. Miller",
journal = SP,
volume = "78",
number = "3",
year = "1999",
pages = "289--307",
email = "rdufour@cdsp.neu.edu,elmiller@ece.neu.edu",
}
@InProceedings{dut:algorithm,
title = "An Implementation of the ``algorithme {\`a} trous'' to
Compute the Wavelet Transform",
author = "P. Dutilleux",
pages = "298--304",
crossref = "com-gro-tch:wavelets",
abstract = "",
}
@Unpublished{edw:discrete,
title = "Discrete Wavelet Transforms: Theory and
Implementation",
author = "Tim Edwards",
note = "Deptartment of Statistics, Stanford University",
year = "1991",
email = "tim@sinh.stanford.edu",
abstract = "This includes a brief introduction to wavelets in
general and the discrete wavelet transform in
particular, covering a number of implementation issues
that are often missed in the literature. A hardware
implementation on a commercially available DSP system
is described along with a program listing to show how
such an implementation can be simulated.",
}
@Article{efr-mor:stein,
title = "Data Analysis Using {S}tein's Estimator and Its
Generalizations",
author = "Bradley Efron and Carl Morris",
journal = JASA,
volume = "70",
number = "350",
year = "1975",
pages = "311--319",
}
@Article{efr:overcome,
title = "How to overcome the curse of long-memory errors",
author = "Efromovich, S.",
journal = IEEETIT,
volume = "45",
number = "5",
year = "1999",
pages = "1735--1741",
author = "Long-memory errors dramatically slow down the
convergence of minimax risks in a fixed design
nonparametric regression. The problem becomes even
more complicated for the case of adaptive
estimation. This defines the curse of long-memory
errors. I show that using a random design, instead
of a fixed one, allows one to overcome this curse
and make familiar data-driven estimators
robust. Moreover, the result holds for a wide class
of nonstationary errors with bounded moments
(including bounded deterministic errors). Possible
extensions are discussed.",
}
@Article{efr:quasi-linear,
title = "Quasi-linear wavelet estimation",
author = "Efromovich, S.",
journal = JASA,
volume = "94",
number = "445",
year = "1999",
pages = "189--204",
keywords = "adaptation asymptotic besov space data compression
filtering monotone function Monte Carlo
nonparametric regression rate optimality sharp
optimality small sample",
abstract = "The main paradigm of the modern wavelet theory of
spatial adaptation formulated by Donoho and
Johnstone is that there is a divergence between the
linear minimax adaptation theory and the heuristic
guiding algorithm development that leads to the
necessity of using strongly nonlinear adaptive
thresholded methods. On the other hand, it is well
known that linear adaptive estimates are the best
whenever an estimated function is smooth. Is it
possible to suggest a quasi-linear wavelet estimate,
by adding to a linear adaptive estimate a minimal
number of nonlinear terms on finest scales, that
offers advantages of linear adaptive estimates and
at the same time matches asymptotic properties of
strongly nonlinear procedures like the benchmark
SureShrink? The answer is ``yes,'' and we discuss
quasi-linear estimation both theoretically and via a
Monte Carlo study. In particular, I show that,
asymptotically, a quasi-linear procedure not only
matches properties of SureShrink over the Besov
scale, but also allows us to relax familiar
assumptions and solve a long standing problem of
rate and sharp optimal estimation of monotone
functions. For the case of small sample sizes and
functions that contain spiky/jumps parts and smooth
parts, a quasi-linear estimate performs
exceptionally well in terms of visual aesthetic
appeal, approximation, and data compression.",
}
@InProceedings{erd-bao-che:interpolation,
title = "Wavelet Interpolation: {F}rom Orthonomal To The
Oversampled Wavelet Transform",
author = "Nurgun Erdol and Feng Bao and Zajing Chen",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing",
volume = "2",
pages = "1093--1096",
year = "1995",
note = "9-12 May 1995, Detroit, MI, USA",
keywords = "oversampled wavelet transform. wavelet interpolation.
orthonormal wavelet transform. signal representation.
aliasing. decimation stage. signal resolution. signal
processing. wideband correlation processing. time
alignment sensitivity. nonorthogonal wavelet transform.
redundancy. wavelet transform coefficients. feature
extraction. filter banks.",
abstract = "The orthonormal wavelet transform is an efficient way
for signal representation since there is no redundancy
in its expression, but due to aliasing in the
decimation stage it lacks the often desired property of
shift invariance. On the other hand, the oversampled or
nonorthogonal wavelet offers a finer resolution in
translation; thus reducing the effect of shift of
origin, it becomes more robust to changes in the
initial phase of the signal. In some areas of signal
processing, such as wideband correlation processing,
sensitivity to time alignment necessitates the use of
the nonorthogonal wavelet transform. The price paid for
the advantage of robustness to shifting is the
introduction of redundancy in the expression. In many
applications, both of these two properties are needed
in different stages of signal processing. Thus there is
a need to know the conditions under which the redundant
and nonorthonormal wavelet transform coefficients can
be derived from the orthonormal wavelet transform
coefficients. The answer provides us with a convenient
way to switch between these two forms: the orthonormal
wavelet for efficient expression, and the nonorthogonal
one whenever it is necessary for feature extraction.",
}
@InProceedings{erd-bao:use,
title = "{U}se of shift variance of the wavelet transform for
signal detection",
booktitle = "Sixth IEEE Digital Signal Processing Workshop",
year = "1994",
author = "N. Erdol and Bao. Feng",
note = "2-5 Oct. 1994, Yosemite National Park, CA, USA",
abstract = "Characterizes signals according to the degree with
which a time shift affects their wavelet series
coefficients and develops a measure called the `shift
index' to quantify that effect. The authors argue that
the shift index can be used to locate, separate and
cluster and/or detect pulse like signals with random
arrival times. Examples are given to verify the
established theory.",
keywords = "wavelet transform. signal detection. shift variance.
time shift. wavelet series coefficients. shift index.
pulse like signals. random arrival times.",
}
@Article{esk-etal:seperating,
title = "Separating different scales of motion in time series
of meteorological variables",
author = "Robert E. Eskridge and Jia-Yeong Ku and S. Trivikrama
Rao and P. Steven Porter and Igor G. Zurbenko",
journal = BAMetS,
volume = "78",
number = "7",
year = "1997",
pages = "1473--1484",
abstract = "The removal of synoptic and seasonal signals from time
series of meteorological variables leaves datasets
amenable to the study of trends, climate change, and
the reasons for such trends and changes. In this paper,
four techniques for separating different scales of
motion are examined and their effectiveness compared.
These techniques are PEST, anomalies, wavelet
transform, and the Kolmogorov-Zurbenko (KZ) filter. It
is shown that PEST and anomalies do not cleanly
separate the synoptic and seasonal signals from the
data as well as the other two methods. The KZ filter
method is shown to have the same level of accuracy as
the wavelet transform method. However, the KZ filter
method can be applied to datasets with missing
observations and is much easier to use than the wavelet
transform method.",
}
@Article{fan-hal-mar-pat:adaptation,
title = "Adaptation to high spatial inhomogeneity using
wavelet methods",
author = "J. Q. Fan and P. Hall and M. A. Martin and P. Patil",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "85--102",
keywords = "convergence rate. fine-scale. local
adaptivity. resolution. wavelet",
abstract = "Many of the signals to which waselet methods are
applied, including those encountered in simulation
experiments, are essentially smooth but contain a
small number of high-frequency episodes such as
spikes. In principle it is possible to employ a
different amount of smoothing at different spatial
locations, but in the context of wavelets this is so
awkward to implement that it is not really
practicable. Instead, it is attractive to select the
primary resolution level (or smoothing parameter) so
as to give good performance for smooth parts of the
signal. While this is readily accomplished using a
cross-validation argument., it is unclear whether it
has a deleterious impact on performance at
high-frequency episodes. In this paper we show that
it does not. We derive upper and lower bounds to
pointwise rates of convergence for functions whose
`spikiness' increases with sample size. (This allows
us to model contexts where wavelet methods have to
work hard to recover high-frequency events.) We show
that, in order to achieve optimal rates of
convergence, it is necessary for the primary
resolution level of the empirical wavelet transform
to vary with location, sometimes
extensively. nevertheless, the convergence rate
penalty incurred through using a non-varying
resolution level, chosen to provide good performance
for coarse-scale features, equals a factor that is
less than the logarithm of sample size.",
}
@Article{fan-hal-mar-pat:local,
journal = JASA,
volume = "91",
number = "433",
year = "1996",
pages = "258--266",
title = "{O}n local smoothing of nonparametric curve
estimators",
author = "J. Q. Fan and P. Hall and M. A. Martin and P. Patil",
abstract = "We develop new local versions of familiar smoothing
methods; such as cross-validation and smoothed
cross-validation, in the contexts of density estimation
and regression. These new methods are locally adaptive
in the sense that they capture smooth local
fluctuations in the curve by using smoothly varying
bandwidths that change as the character of the curve
changes. Moreover, the new methods are accurate, easy
to apply, and computationally expedient.",
keywords = "density-estimation. bandwidth choice.
cross-validation.",
}
@Article{fan-lin:curves,
title = "Test of significance when data are curves",
author = "Fan, J. Q. and Lin, S. K.",
journal = JASA,
volume = "93",
number = "443",
year = "1998",
pages = "1007--1021",
keywords = "adaptive analysis of variance adaptive Neyman rest
functional data repeated measurements thresholding
wavelets",
abstract = "With modern technology, massive data can easily
be collected in a form of multiple sets of
curves. New statistical challenge includes testing
whether there is any statistically significant
difference among these sets of curves. In this
article we propose some new tests for comparing
two groups of curves based on the adaptive Neyman
test and the wavelet thresholding techniques
introduced earlier by Fan. We demonstrate that these
tests inherit the properties outlined by Fan and
that they are simple and powerful for detecting
differences between two sets of curves. We then
further generalize the idea to compare multiple sets
of curves, resulting in an adaptive high-dimensional
analysis of variance, called HANOVA. These newly
developed techniques are illustrated by using a
dataset on pizza commercials where observations are
curves and an analysis of cornea topography in
ophthalmology where images of individuals are
observed. A simulation example is also presented to
illustrate the power of the adaptive Neyman test.",
}
@Article{fan:test,
journal = JASA,
volume = "91",
number = "434",
year = "1996",
pages = "674--688",
title = "{T}est of significance based on wavelet thresholding
and {N}eyman's truncation",
author = "J. Q. Fan",
abstract = "Traditional nonparametric tests, such as the
Kolomogorov-Smirnov test and the Cramer-Von Mises test,
are based on the empirical distribution functions.
Although these tests possess root-n consistency, they
effectively use only information contained in the low
frequencies. This leads to low power in detecting fine
features such as sharp and short aberrants as well as
global features such as high-frequency alternations.
The drawback can be repaired via smoothing-based test
statistics. In this article we propose two such kind of
test statistics based on the wavelet thresholding and
the Neyman truncation. We provide extensive evidence to
demonstrate that the proposed tests have higher power
in detecting sharp peaks and high frequency
alternations, while maintaining the same capability in
detecting smooth alternative densities as the
traditional tests. Similar conclusions can be made for
two-sample nonparametric tests of distribution
functions. In that case, the traditional linear rank
tests such as the Wilcoxon test and the Fisher-Yates
test have low power in detecting two nearby densities
where one has local features or contains high-frequency
components, because these procedures are essentially
testing the uniform distribution based on the sample
mean of rank statistics. In contrast, the proposed
tests use more fully the sampling information and have
better ability in detecting subtle features.",
keywords = "adaptive Neyman test. goodness-of-fit.
hard-thresholding parameter. soft-thresholding
parameter. two-sample test. wavelet thresholding.",
}
@InProceedings{far-bro:applications,
title = "Applications of Time-Frequency and Time-Scale
Transforms to Ultra-Wideband Radar Transient Signal
Detection",
author = "Monique P. Fargues and William A. Brooks",
booktitle = "Advanced Signal Processing Algorithms, Architectures,
and Implementations IV",
editor = "Franklin T. Luk",
volume = "2027",
organization = SPIE,
year = "1993",
pages = "180--193",
address = "San Diego, California",
abstract = "Compared to conventional radars, ultra-wideband (UWB)
radars are characterized by very large bandwidth and
fine range resolution. Potential applications of this
type of radar include terrain mapping, and target
identification/classification. In this paper we use a
non- stationary approach and analyze UWB radar data
using time- frequency and time-scale transformations.
The time-frequency transformations considered are the
Short-Time Fourier Transform (STFT), the Wigner-Ville
Distribution (WD), the Instantaneous Power Spectrum
(IPS), and the ZAM transform. Two discrete
implementations of the Wavelet Transform (DWT) are also
investigated: the decimated A-trous algorithm proposed
by Holschneider et al, which uses non-orthogonal
wavelets; and the Mallat algorithm, which employs
orthogonal wavelets. The transients under study are UWB
radar returns from a boat (with and without corner
reflector) in the presence of sea clutter, multipath,
and radio frequency interferences (RFI). Results show
that all time-frequency and time-scale transforms
clearly detect the transient radar returns
corresponding to the boat with a corner reflector.
However, as the radar cross section of the target
decreases (boat without a corner reflector), results
change drastically as the RFI component dominates the
signal. Simulations show that the Instantaneous Power
Spectrum may be better adapted for localizing the
transient among the time-frequency techniques studied.
The decimated A-trous algorithm has the best time
resolution of the techniques studied as the return
appears better localized in the scalogram.",
}
@Proceedings{far-hun-vas:wavelets,
title = "Wavelets, fractals, and Fourier transforms",
booktitle = "Wavelets, fractals, and Fourier transforms",
editor = "M. Farge and Julian C. R. Hunt and J. C Vassilicos",
volume = "43",
series = "Institute of Mathematics and Its Applications
conference series",
year = "1993",
publisher = "Clarendon Press",
address = NY,
keywords = "Wavelets, Mathematics, Fractals, Fourier
transformations",
loc = "QA403.3 .W39 1993",
note = "Based on the proceedings of a conference on wavelets,
fractals, and Fourier transforms held at Newnham
College, Cambridge in December 1990",
}
@Article{far-kev-per-goi:turbulence,
journal = PIEEE,
volume = "84",
number = "4",
year = "1996",
pages = "639--669",
title = "{W}avelets and turbulence",
author = "M. Farge and N. Kevlahan and V. Perrier and U.
Goirand",
abstract = "We have used wavelet transform techniques to analyze,
model, and compute turbulent flows. The theory and open
questions encountered in turbulence are presented The
wavelet-based techniques that we have applied to
turbulence problems are explained and the main results
obtained are summarized.",
keywords = "partial-differential equations. two-dimensional
turbulence. statistical equilibrium states.
negative-temperature states. fully-developed
turbulence. perfect fluid-dynamics. reynolds-number.
isotropic turbulence. numerical-solution.
kinetic-equations",
}
@Article{far:AS256,
title = "The Distribution of a Quadratic Form in Normal
Variables",
author = "R. W. Farebrother",
journal = AS,
volume = "39",
number = "2",
pages = "294--309",
year = "1990",
keywords = "Imhof procedure; Koerts-Ambrose algorithm; Linear
combination of chi-squared variables",
}
@Article{far:eigenvalue,
title = "Eigenvalue-{F}ree Methods for Computing the
Distribution of a Quadratic Form in Normal Variables",
author = "R. W. Farebrother",
journal = "Statistische Hefte",
volume = "26",
number = "",
pages = "287--302",
year = "1985",
keywords = "",
}
@Article{far:wavelets,
title = "Wavelet transforms and their applications to
turbulence",
author = "M. Farge",
journal = "Annual Review of Fluid Mechanics",
volume = "24",
year = "1992",
pages = "395--457",
}
@InProceedings{fer-per-swe:spie96,
title = "{LIFTPACK}: {A} software package for wavelet
transforms using lifting",
author = "G. Fern\'{a}ndez and S. Periaswamy and Wim Sweldens",
crossref = "uns-ald-lai:wavelet4",
URL = "http://cm.bell-labs.com/who/wim/papers/spi96.ps",
abstract = "We present LIFTPACK: A software package written in C
for fast calculation of 2D biorthogonal wavelet
transforms using the lifting scheme. The lifting scheme
is a new approach for the construction of biorthogonal
wavelets entirely in the spatial domain, i.e.,
independent of the Fourier Transform. Constructing
wavelets using lifting consists of three simple phases:
the first step or Lazy wavelet splits the data into two
subsets, even and odd, the second step calculates the
wavelet coefficients (high pass) as the failure to
predict the odd set based on the even, and finally the
third step updates the even set using the wavelet
coefficients to compute the scaling function
coefficients (low pass). The predict phase ensures
polynomial cancelation in the high pass (vanishing
moments of the dual wavelet) and the update phase
ensures preservation of moments in the low pass
(vanishing moments of the primal wavelet). By varying
the order, an entire family of transforms can be built.
The lifting scheme ensures fast calculation of the
forward and inverse wavelet transforms that only
involve FIR filters. The transform works for images of
arbitrary size with correct treatment of the
boundaries. Also, all computations can be done
in-place.",
}
@Article{fis:frequency,
title = "Frequency distribution of the values of the
correlation coefficient in samples from an indefinitely
large population",
author = "R. A. Fisher",
journal = BKA,
volume = "10",
year = "1915",
pages = "507--521",
}
@Article{fis:tests,
title = "Tests of significance in harmonic analysis",
author = "R. A. Fisher",
journal = PRSLA,
volume = "125",
year = "1929",
pages = "54--59",
}
@InCollection{fla-gon:from,
title = "From Wavelets to Time-Scale Energy Distributions",
author = "P. Flandrin and P. Gon\c{c}lav{\`e}s",
pages = "309--334",
crossref = "sch-web:recent",
}
@Article{fla:brownian,
title = "Wavelet Analysis and Synthesis of Fractional
{B}rownian Motion",
author = "Patrick Flandrin",
journal = IEEETIT,
volume = "38",
number = "2",
year = "1992",
pages = "910--917",
abstract = "Fractional Brownian motion (FBM) offers a convenient
modeling for nonstationary stochastic processes with
long-term dependencies and 1/f-type spectral behavior
over wide ranges of frequencies. Statistical
self-similarity is an essential feature of FBM and
makes natural the use of wavelets for both its analysis
and its synthesis. A detailed second-order analysis is
carried out for wavelet coefficients of FBM. It reveals
a stationary structure at each scale and a power-law
behavior of the coefficients' variance from which the
fractal dimension of FBM can be estimated. Conditions
for using orthonormal wavelet decompositions as
approximate whitening filters are discussed,
consequences of discretization are considered, and some
connections between the wavelet point of view and
previous approaches based on length measurements
(analysis) or dyadic interpolation (synthesis) are
briefly pointed out.",
}
@Article{fos:unevenly,
title = "Wavelets for Period Analysis of Unevenly Sampled Time
Series",
author = "Grant Foster",
journal = AnJ,
volume = "112",
number = "4",
year = "1996",
pages = "1709--1729",
email = "gfoster@aavso.org",
}
@InProceedings{fou:blocking,
title = "Wavelet analysis of observed geopotential and wind:
{B}locking and local energy coupling across scales",
author = "Aim\'{e} Fournier",
crossref = "uns-ald-lai:wavelet4",
email = "fournier@cloudy.geology.yale.edu",
abstract = "Atmospheric blocking during three unusual winter
months is studied by multiresolution analysis and a
wavelet based adaptation of traditional Fourier series
based energetics. We demonstrate that blocking, in part
a large and localized meteorological phenomenon, is
largely described by just the largest scale part of the
multiresolution analysis. New forms of the transfer
functions of kinetic energy with the mean and eddy
parts of the atmospheric circulation are introduced.
These quantify the spatially localized conversion of
energy between scales. A new accounting method for
wavelet indexed transfers permits the introduction of a
physically meaningful localized scale flux function.
These techniques are applied to the data, and some
support is found for the hypothesis that blocking is
partially maintained by an inverse cascade.",
}
@Unpublished{fou:introduction,
title = "An introduction to orthonormal wavelet analysis with
shift invariance: {A}pplication to observed
atmospheric-blocking spatial structure",
author = "Aim\'{e} Fournier",
year = "1999",
note = "Submitted to the {\em Journal of the Atmospheric
Sciences}",
abstract = "Orthonormal wavelet analysis (OWA) is a special form
of wavelet analysis which is especially suitable for
analyzing spatial structures, such as atmospheric
fields. For this purpose, OWA is more efficient and
accurate than the nonorthogonal wavelet analysis
(NWA) which has been introduced to the
meteorological community in recent years, and which
is more suitable for ``making time series sing.''
Since NWA is strictly correct only for infinite
domains, OWA must be derived from NWA by use of
appropriate boundary conditions, in this case, by
periodization of OWA on an infinite domain. OWA is
not translation invariant, unlike NWA. Two remedies
are to use all possible translations, known as the
Stationary Wavelet Transform, or else to use a
`best' translation, known as the Best Shift OWA. OWA
is a generalization of Fourier series, and the
associated multiresolution analysis (MRA) is a
generalization of Reynolds averaging. Like these,
OWA/MRA on discrete and continuous domains satisfy
analogous identities arithmetically exactly, unlike
NWA. OWA/MRA is more efficient than Fourier series
for analyzing nearly-singular synthetic functions,
and also sequences of observed geopotential height
maps which contain atmospheric blocking. Close to or
more than 90% of the spatial variance of
latitude-band averaged geopotential height, averaged
over five different blocking events, is
reconstructed by only two wavelets using best
shift. This is comparable to EOF analysis, but is
much faster and less data-dependent. All of the
basic OWA programs are freely available for MATLAB
(R), in the package WaveLab (c).",
}
@InProceedings{fou:lower,
title = "Wavelet representation of lower-atmospheric long
nonlinear wave dynamics, governed by the
{B}enjamin-{D}avis-{O}no-{B}urgers equation",
author = "Aim\'{e} Fournier",
crossref = "szu:wavelet2",
pages = "672--681",
}
@InProceedings{fou:simulated,
title = "Wavelet multiresolution analysis of numerically
simulated 3{D} radiative convection",
author = "Aim\'{e} Fournier",
pages = "642--653",
crossref = "szu:wavelet3",
email = "fournier@cloudy.geology.yale.edu",
abstract = "A wavelet multiresolution analysis is performed on
atmospheric fields simulated by a multilevel
3-dimensional atmospheric boundary layer
model. Wavelet cospectra of the vertical wind and
potential temperature are calculated and compared
with radial Fourier cospectra. The former indicate
most of the field variance to have horizontal scales
roughly equal to the vertical scale, as should be
the case for convectively driven turbulence. Fourier
spectra exhibit a -3 power law, suggesting that the
statistics may depend only on a quantity with units
of time. Observations of time-and scale-dependent
structures suggest certain physical mechanisms at
work. The multiresolution analysis analogue of
turbulent energy equations are formulated. This
framework supports the proposed physical
mechanisms.",
}
@Article{fri-gro-tch:gaps,
title = "Wavelet analysis of signals with gaps",
author = "Frick, P. and Grossmann, A. and Tchamitchian, P.",
journal = JMP,
volume = "39",
number = "8",
year = "1998",
pages = "4091--4107",
abstract = "A recently introduced algorithm [Frick et al.,
Astrophys. J. 483, 426 (1997)] of spectral analysis
of data with gaps via a modified continuous wavelet
transform is developed and studied. This algorithm
is based on a family of functions called ``gapped
wavelets'' which fulfill the admissibility condition
on the gapped support. The wavelet family is
characterized by an additional parameter which
should be calculated for every scale and
position. Three theorems concerning the properties
of gapped wavelet transform are formulated and
proved. They affirm the global stability of the
algorithm as well as its stability in both limits of
large and small scales. These results are
illustrated by some numerical examples, which show
that the algorithm really attenuates the artifacts
coming from gaps (and/or boundaries), and is
particularly efficient at small and large scales.",
}
@InProceedings{gag:numerical-results,
title = "Wavelet filtering of speckle noise -- some numerical
results",
author = "Langis Gagnon",
booktitle = "Proceedings of the Conference Vision Interface",
year = "1999",
pages = "???--???",
email = "langis.gagnon@crim.ca",
URL = "http://www.crm.umontreal.ca/~lgagnon/articles/vi99.pdf",
}
@Article{gal-hut:terrain,
title = "Scale dependence in terrain analysis",
author = "J. C. Gallant and M. F. Hutchinson",
journal = "Mathematics and Computers in Simulation",
volume = "43",
number = "3--6",
month = mar,
year = "1997",
pages = "313--321",
keywords = "elevation",
abstract = "Topographic attributes computed from digital elevation
models are dependent on the resolution of the elevation
data from which they are computed. A regular
rectangular grid is not an ideal representation of
topographic surfaces for the study of scale effects.
Spectral and wavelet techniques are obvious
alternatives but have several deficiencies,
particularly in their use of oscillatory basis
functions. The positive wavelet representation has very
attractive properties of localisation and feature
representation. Preliminary application to
one-dimensional topographic data (profiles) yields
useful results, including the identification of changes
in topographic structure with scale. Extension to
two-dimensional analysis will allow quantification of
characteristic shapes, scales and orientations in the
landscape.",
}
@Article{gam:wavelet,
title = "Wavelet transform analysis of the length of the day
and {E}l-{N}i{\~n}o/{S}outhern {O}scillation
variations at intraseasonal and interannual time
scales",
author = "Gambis, D.",
journal = AG,
volume = "10",
number = "",
year = "1992",
pages = "429--437",
}
@Article{gao-bru:firm,
title = "{W}ave{S}hrink with Firm Shrinkage",
author = "Hong-Ye Gao and Andrew Bruce",
journal = SSin,
volume = "7",
number = "4",
year = "1997",
pages = "855--874",
URL = "ftp://ftp.statsci.com/pub/gao/firm.ps.Z",
keywords = "Bias Estimation; Confidence Interval; Firm Shrinkage;
Minimax Thresholds; Non-parametric Regression; Signal
De-noising; Trend Estimation; Variance Estimation;
Wavelet Transform; WaveShrink",
abstract = "Donoho and Johnstone's WaveShrink procedure has proven
valuable for signal de-noising and non-parametric
regression. WaveShrink has very broad asymptotic
near-optimality properties. In this paper, we introduce
a new shrinkage scheme, {\em firm}, which generalizes
the hard and soft shrinkage proposed by Donoho and
Johnstone. We derive minimax thresholds and provide
formulas for computing the pointwise variance, bias,
and risk for WaveShrink with firm shrinkage. We study
the properties of the shrinkage functions, and
demonstrate that firm shrinkage offers advantages over
both hard shrinkage (uniformly smaller risk and less
sensitivity to small perturbations in the data) and
soft shrinkage (smaller bias and overall $L_2$ risk).
Software is provided to reproduce all results in this
paper.",
}
@Article{gao-li:coherent,
journal = JAM,
volume = "32",
number = "11",
year = "1993",
pages = "1717--1725",
title = "{W}avelet analysis of coherent structures at the
atmosphere-forest interface",
author = "W. Gao and BL. Li",
abstract = "Wavelet studies were used for the turbulent data
obtained inside and over a deciduous forest to
investigate spatial and scale properties of a coherent
structure in the area. Discrete warm and cool centers
are linked to organized updrafts and downdrafts. Their
patterns are alike, but the magnitudes vary at various
heights. Temperature structures over the canopy possess
a shorter duration, but the rate of reduction in the
time scale with increasing height seems proportional to
the rise in mean wind speed.",
}
@Article{gao:choice,
title = "Choice of Thresholds for Wavelet Shrinkage Estimate of
the Spectrum",
author = "Hong-Ye Gao",
journal = JTSA,
volume = "18",
number = "3",
year = "1997",
pages = "231--251",
URL = "ftp://ftp.mathsoft.com/pub/wavelets/wavethresh.ps",
keywords = "Log Spectrum Estimation; Orthogonal Wavelet
Transformation; Shrinkage Estimator",
abstract = "We study the problem of estimating the log spectrum of
a stationary Gaussian time series by thresholding the
empirical wavelet coefficients. We propose the use of
thresholds $t_{j,n}$ depending on sample size n,
wavelet basis and resolution level j. At fine
resolution levels (j=1, 2,...), we propose \[ t_{j,n} =
A_j\log n, \] where $A_j$ are level-dependent constants
and at coarse levels (j>>1), \[ t_{j,n} =
\frac{\pi}{\sqrt{3}}\sqrt{\log n}. \] The purpose of
this thresholding level is to make the reconstructed
log-spectrum as nearly noise-free as possible. In
addition to being pleasant from a visual point of view,
the noise-free character leads to attractive
theoretical properties over a wide range of smoothness
assumptions. Previous proposals set much smaller
thresholds and did not enjoy these properties.",
}
@Article{gao:garrote,
title = "Wavelet Shrinkage DeNoising Using Non-Negative
Garrote",
author = "Hong-Ye Gao",
journal = JCGS,
volume = "7",
number = "4",
year = "1998",
pages = "469--488",
URL = "http://www.amstat.org/publications/jcgs/pdf_98/Gao.pdf",
keywords = "Cycle-Spinning; Minimax Threshold; Non-negative
Garrote; Nonparametric Regression; Shrinkage Functions;
Stein's Unbiased Risk Estimate (SURE); Wavelet
Transform",
abstract = "In this paper, we combine Donoho and Johnstone's
Wavelet Shrinkage denoising technique (known as
WaveShrink) with Breiman's non-negative garrote. We
show that the non-negative garrote shrinkage estimate
enjoys the same asymptotic convergence rate as the hard
and the soft shrinkage estimates. For finite sample
simulations, non-negative garrote performs better
(smaller mean-square-error) than both hard and soft,
and comparable to the firm shrinkage. We derive the
minimax thresholds for the non-negative garrote. We
study the threshold selection procedure based on
Stein's Unbiased Risk Estimate (SURE) for both
non-negative garrote and soft shrinkages. We propose a
new threshold selection procedure based on combining
Coifman and Donoho's cycle-spinning and SURE. We call
our new procedure SPINSURE. We use examples to show
that SPINSURE is more stable than SURE: smaller
standard deviation and smaller range.",
}
@Unpublished{gao:heteroscedastic,
title = "Wavelet Shrinkage Estimates For Heteroscedastic
Regression Models",
author = "Hong-Ye Gao",
note = "Statistical Sciences Division, MathSoft, Inc",
year = "1997",
URL = "ftp://ftp.statsci.com/pub/gao/wsshd.ps.Z",
keywords = "Heteroscedasticity; Nonparametric Regression; Running
MAD; Wavelet Transform; Variance Estimation.",
abstract = "We extend Donoho and Johnstone's wavelet shrinkage
smoothing technique (known as WaveShrink) to handle
data with heteroscedastic noise. We first show that if
the noise variances are known, WaveShrink estimate
achieves the same near-optimal convergence rate as in
the white noise case. We then propose a procedure for
estimating the noise variances. Our procedure is based
on applying running MAD (Median Absolute Deviation from
the median) to the non-decimated finest level wavelet
coefficients. We apply our technique to various
numerical examples.",
}
@Unpublished{gao:isontonic,
title = "Wavelets and Isotonic Regression",
author = "Hong-Ye Gao",
note = "Statistical Sciences Division, MathSoft, Inc",
year = "199?",
URL = "ftp://ftp.statsci.com/pub/gao/isotonic.ps.Z",
keywords = "Grenander Estimator; Isotonic Regression; Monotone
Curve; Orthogonal Wavelet Transformation; Shrinkage
Estimator",
abstract = "Consider the following isotonic regression model: \[
y_i = f(t_i) + z_i\] where $f$ is only known to be a
decreasing function and $\{z_i\}$ are iid Gaussian with
mean zero and variance $\sigma^2$. We propose a simple
thresholding procedure based on the fact that the
wavelet coefficients for $f$, under Haar basis, are
non-negative. We show that our estimator is competitive
with the Grenander estimator both theoretically and
numerically (in the sense of mean-square-error).",
}
@Unpublished{gao:selection,
title = "Threshold Selection in {W}ave{S}hrink",
author = "Hong-Ye Gao",
note = "Statistical Sciences Division, MathSoft, Inc",
year = "1997",
URL = "ftp://ftp.statsci.com/pub/gao/threshold.ps.Z",
keywords = "Cycle-Spinning; Minimax Threshold; Non-negative
Garrote; Nonparametric Regression; Shrinkage Functions;
Stein's Unbiased Risk Estimate (SURE); Wavelet
Transform; WaveShrink",
abstract = "Donoho and Johnstone's wavelet shrinkage denoising
technique (known as WaveShrink) consists three steps:
(1) transform data into wavelet domain; (2) shrink the
wavelet coefficients; and (3) transform the shrunk
coefficients back. The choice of shrinkage function and
thresholds in step (2) plays an important role for
WaveShrink both theoretically and in practice. In this
paper, we discuss the issue of threshold selection in
WaveShrink. We first review the threshold selection
procedure based minimax thresholds and Stein's Unbiased
Risk Estimate (SURE). We then propose a new threshold
selection procedure based on combining Coifman and
Donoho's cycle-spinning and SURE. We call our new
procedure SPINSURE. We use examples to show that
SPINSURE is numerically more stable than SURE: smaller
standard deviation and smaller range. Various
comparisons with the ideal and minimax thresholds are
also presented.",
}
@Unpublished{gao:spectral,
title = "Spectral Density Estimation via Wavelet Shrinkage",
author = "Hong-Ye Gao",
note = "Statistical Sciences Division, MathSoft, Inc",
year = "1996",
URL = "ftp://ftp.statsci.com/pub/gao/spec.ps.Z",
keywords = "Non-Gaussian Model; Periodized Meyer Wavelets;
Shrinkage Estimator; Spectral Density Estimation;
Wavelet Transform",
abstract = "We study the problem of estimating the spectral
density of a stationary Gaussian time series. We use
an orthogonal wavelet system whose members are
periodic functions and have a finite number of
non-zero Fourier coefficients -- periodized Meyer
wavelets. We apply shrinkage rules to the empirical
wavelet coefficients. We show that estimates based
on thresholds $t_{j,n} = \lm_j\log n$ for certain
$\lm_j$, with $n$ the sample size, have near-optimal
$L_2$ convergence rates, over any Besov class in a
wide range. In some cases, which includes the Bump
Algebra, wavelet shrinkage procedures significantly
outperform classical linear procedures, such as
window methods and AR approximation methods.",
}
@PhdThesis{gao:thesis,
title = "Wavelet Estimation of Spectral Densities in Time
Series Analysis",
author = "Hong-Ye Gao",
school = "University of California, Berkeley",
year = "1993",
}
@Unpublished{gen-sel-whi:differentiating,
title = "Differentiating intraday seasonalities through
wavelet multi-scaling",
author = "R. Gen\c{c}ay and F. Sel\c{c}uk and B. Whitcher",
year = "1999",
note = "submitted",
}
@Unpublished{gen-sel-whi:high-frequency,
title = "Wavelet Scale Analysis of High-Frequency Foreign
Exchange Rates",
author = "R. Gen\c{c}ay and F. Sel\c{c}uk and B. Whitcher",
year = "2000",
note = "submitted",
}
@Article{ger-har-mas:fractal,
title = "Fractal functions and wavelet expansions based on
several scaling functions",
author = "Jeffrey S. Geronimo and Douglas P. Hardin and Peter R.
Massopust",
journal = JAT,
volume = "78",
number = "3",
year = "1994",
pages = "373--401",
}
@InProceedings{gil-wil-fel:visualizing,
title = "Visualizing multifractal scaling behavior: {A}
simple coloring heuristic",
author = "A. C. Gilbert and W. Willinger and A. Feldman",
booktitle = "Conference Record of The Thirty-Second Asilomar
Conference on Signals, Systems and Computers",
volume = "1",
year = "1998",
pages = "715--722",
email = "agilbert@research.att.com, walter@research.att.com,
anja@research.att.com",
URL = "http://www.research.att.com/~agilbert/ps.files/asilomar98.ps.Z",
}
@Article{gil:trend,
title = "Testing for the onset of trend, using wavelets",
author = "Scott D. Gilbert",
journal = JTSA,
volume = "20",
number = "5",
year = "1999",
pages = "513--526",
}
@InCollection{gof:wavelets,
title = "Wavelets in macroeconomics: {A}n introduction",
author = "W. L. Goffe",
booktitle = "Computational Techniques for Econometrics and
Economic Analysis",
editor = "D. A. Belsley",
publisher = "Kluwar Academic Publishers",
address = "Dordrecht",
series = "Advances in Computational Economics",
volume = "3",
year = "1993",
pages = "???--???",
}
@InProceedings{gon-abr:multiple-window,
title = "Multiple-window wavelet transform and local scaling
exponent estimation",
author = "P. Gon\c{c}alv{\`e}s and P. Abry",
booktitle = "Proceedings of the IEEE International Conference on
Acoustics, Speech, and Signal Processing",
volume = "4",
year = "1997",
pages = "3433--3436",
email = "paulo.goncalves@inria.fr,
pabry@physique.ens-lyon.fr",
abstract = "We propose here a multiple-window wavelet transform
for the purpose of identifying non-stationary
self-similar structures in random processes and
estimating the time-varying scaling exponent H(t)
that controls the local regularity and correlation
of the process. More specifically, our final aim is
to be able to track even rapidly varying
trajectories (t,H(t)). The solution described here
combines analysis obtained from scalograms computed
with a set of multi-windows designed so as to
satysfy to a decorrelation condition. We derive here
the statistics for the estimate of H(t), compare it
against numerical simulations and show that we
obtain a substantial reduction of variance in
estimation, without introducing bias.",
}
@InCollection{gon-fla:bilinear,
title = "Bilinear Time-Scale Analysis Applied to Local
Scaling Exponents Estimation",
author = "P. Gon\c{c}alv{\`e}s and P. Flandrin",
pages = "271--276",
crossref = "mey-roq:progress",
}
@InProceedings{gon-fla:scaling,
title = "Scaling exponents estimation from time-scale energy
distributions",
author = "P. Gon\c{c}alv{\`e}s and P. Flandrin",
booktitle = "Proceedings of the IEEE International Conference on
Acoustics, Speech, and Signal Processing",
volume = "5",
year = "1992",
pages = "157--160",
}
@Unpublished{gon-etal:financial,
title = "The Wavelet Transform for Filtering Financial Data
Streams",
author = "Zheng Gonghui and Jean-Luc Stark and Jonathan
Campbell and Fionn Murtagh",
year = "1998",
note = "Submitted to {\em Journal of Computational
Intelligence in Finance}",
}
@InProceedings{gon-rie-bar:simple,
title = "Simple Statistical Analysis of Wavelet-based
Multifractal Spectrum Estimation",
author = "P. Gon\c{c}alv{\`e}s and R. H. Riedi and
R. G. Baraniuk",
booktitle = "Conference Record of The Thirty-Second Asilomar
Conference on Signals, Systems and Computers",
volume = "?",
year = "1998",
pages = "???--???",
URL = "http://www-dsp.rice.edu/~riedi/cv_frame.html",
abstract = "The multifractal spectrum characterizes the scaling
and singularity structures of signals and proves
useful in numerous applications, from network
traffic analysis to turbulence. Of great concern is
the estimation of the spectrum from a finite data
record. In this paper, we derive asymptotic
expressions for the bias and variance of a
wavelet-based estimator for a fractional Brownian
motion (fBm) process. Numerous numerical simulations
demonstrate the accuracy and utility of our
results.",
}
@Article{gou-auv-bag:dwarfs,
title = "Wavelet Analysis of Pulsating White Dwarfs",
author = "M. J. Goupil and M. Auvergne and A. Baglin",
journal = AandA,
volume = "250",
number = "1",
year = "1991",
pages = "89--98",
abstract = "Parts of light curves of two variable white dwarfs,
Giclas 191-16 (BR Cam) and PG 1351+489 (EM UMa), are
investigated by means of a wavelet analysis. This
time-frequency analysis decomposes the light curves
into their different oscillating components whose
temporal behaviors are then individually studied. In
addition to an oscillation of large amplitude, small
amplitude oscillations are thereby clearly emphasized
for both stars. Amplitude variations are found for most
detected oscillations with periods of modulation as
long or greater than the time intervals of the
corresponding runs. A wavelet analysis of a comparison
star gives the quality of the night in localizing
perturbative atmospheric events.",
}
@Article{gra:introduction,
title = "An introduction to wavelets",
author = "Amara Graps",
journal = IEEECSE,
volume = "2",
number = "2",
year = "1995",
pages = "50--61",
URL = "ftp://ftp.best.com/pub/agraps/papers/IEEEwavelet.ps.gz",
keywords = "wavelets, scale-based analysis, mathematical
requirements, data represention, packet techniques,
applications, data analysis, discretely sampled
time-series data",
abstract = "Wavelets were developed independently by
mathematicians, quantum physicists, electrical
engineers and geologists, but collaborations among
these fields during the last decade have led to new and
varied applications. What are wavelets, and why might
they be useful to you? The fundamental idea behind
wavelets is to analyze according to scale. Indeed, some
researchers feel that using wavelets means adopting a
whole new mind-set or perspective in processing data.
Wavelets are functions that satisfy certain
mathematical requirements and are used in representing
data or other functions. Most of the basic wavelet
theory has now been done. The mathematics have been
worked out in excruciating detail, and wavelet theory
is now in the refinement stage. This involves
generalizing and extending wavelets, such as in
extending wavelet packet techniques. The future of
wavelets lies in the as-yet uncharted territory of
applications. Wavelet techniques have not been
thoroughly worked out in such applications as practical
data analysis, where, for example, discretely sampled
time-series data might need to be analyzed. Such
applications offer exciting avenues for exploration.",
}
@Article{gre-gie-lip:invariance,
title = "Translational invariance in turbulent cascade models",
author = "M. Greiner and J. Giesemann and P. Lipa",
journal = PRE,
volume = "56",
number = "4",
year = "1997",
pages = "4263--4274",
URL = "http://ojps.aip.org/journal_cgi/getabs?KEY=PLEEE8&cvips=PLEEE8000056000004004263000001&gifs=No",
keywords = "fully-developed turbulence hydrodynamic turbulence
exact resummations wavelet correlations",
abstract = "Due to the underlying hierarchical structure, spatial
correlation functions calculated from multiplicative
cascade models are not translationally invariant. A
scheme is presented that restores translational
invariance by averaging over the experimentally unknown
spatial location of cascade realizations with respect
to the observation window. The impact of this scheme on
multiplier distributions for the energy dissipation
field in fully developed turbulence is analyzed; only
the experimental multiplier distribution is found to be
invariant under a wide range of scales.",
}
@Article{gre-ros:fast,
title = "A fast wavelet-based Karhunen-Loeve transform",
author = "Greenshields, I. R. and Rosiene, J. A.",
journal = PR,
volume = "31",
number = "7",
year = "1998",
pages = "839--845",
abstract = "The paper describes the role of the standard wavelet
decomposition in computing a fast Karhunen-Loeve
transform. The standard wavelet decomposition (which we
show is different from the conventional wavelet
transform) leads to a highly sparse and simply structured
transformed version of the correlation matrix which can
be easily subsetted (with little loss of Frobenius norm).
The eigenstructure of this smaller matrix can be
efficiently computed using standard algorithms such as
QL. Finally, we provide an example of the use of the
efficient transform by classifying a 219-channel AVIRIS
image with respect to its eigensystem.",
}
@InCollection{gre:cross-validation,
title = "Wavelet basis selection for regression by
cross-validation",
author = "Seth A. Greenblatt",
booktitle = "Computational Approaches to Economic Problems",
editor = "H. M. Amman and B. Rustem and A. B. Whinston",
publisher = "Kluwar Academic Publishers",
address = "Dordrecht",
series = "Advances in Computational Economics",
volume = "6",
year = "1997",
pages = "39--55",
}
@InCollection{gre:outlier,
title = "Wavelets in econometrics: {A}n application to
outlier testing",
author = "Seth A. Greenblatt",
booktitle = "Computational Economic Systems: Models, Methods \&
Econometrics",
editor = "M. Gilli",
publisher = "Kluwar Academic Publishers",
address = "Dordrecht",
series = "Advances in Computational Economics",
volume = "5",
year = "1996",
pages = "139--160",
}
@InProceedings{gro-kro-mar:reading,
title = "Reading and understanding continuous wavelet
transforms",
author = "A. Grossmann and R. Kronland-Martinet and J. Morlet",
pages = "2--20",
crossref = "com-gro-tch:wavelets",
keywords = "wavelets",
abstract = "An introduction to continuous wavelet transforms and a
description of the representation methods that have
evolved. Also discusses the influence of the choice of
the wavelet in the interpretation of wavelet
transforms.",
}
@Article{gro-mor:hardy,
title = "Decomposition of {H}ardy Functions into Square
Integrable Wavelets of Constant Shape",
author = "A. Grossmann and J. Morlet",
journal = SIAMJMA,
volume = "15",
number = "4",
year = "1984",
pages = "723--736",
abstract = "",
}
@Article{gru-wal:seismic,
title = "{C}haracterizing seismic time series using the
discrete wavelet transform",
author = "H. J. Grubb and A. T. Walden",
journal = GP,
volume = "45",
number = "2",
year = "1997",
pages = "183--205",
abstract = "The discrete wavelet transform (DWT) has potential as
a tool for supplying discriminatory attributes with
which to characterize or cluster groups of seismic
traces in reservoir studies. The wavelet transform has
the great advantage over the Fourier transform in being
able to better localize changes. The multiscale nature
and structure of the DWT leads to a method of display
which highlights this and allows comparison of changes
in the transform with changing data. Many different
sorts of wavelet exist and it is found that the quality
of reconstruction of a seismic trace segment, using
some of the coefficients, is dependent on the choice of
wavelet, which leads us to consider choosing a wavelet
under a 'best reconstruction' criterion. Location
shifts, time zero uncertainties, are also shown to
affect the transform, as do truncations, resampling,
etc. Using real data, examples of utilizing the DWT
coefficients as attributes for whole trace segments or
fractional trace segments are given. Provided the DWT
is applied consistently, for example with a fixed
wavelet, and non-truncated data, the transform produces
useful results. Care must be exercised if it is applied
to data of different lengths. However, as the algorithm
is refined and improved in the future, the DWT should
prove increasingly useful.",
keywords = "projection pursuit, sampling theory, propagation,
signal",
}
@MastersThesis{guo:msthesis,
title = "Theory and Applications of the Shift-Invariant,
Time-Varying and Undercimated Wavelet Transforms",
author = "Haitao Guo",
year = "1995",
pages = "144",
school = "Electrical and Computer Engineering Department, Rice
University",
URL = "http://www-dsp.rice.edu/~harry/paper/ms.ps.Z",
email = "harry@ece.rice.edu",
abstract = "In this thesis, we generalize the classical discrete
wavelet transform, and construct wavelet transforms
that are shift-invariant, time-varying, undecimated,
and signal dependent. The result is a set of powerful
and efficient algorithms suitable for a wide variety of
signal processing tasks, e.g., data compression, signal
analysis, noise reduction, statistical estimation, and
detection. These algorithms are comparable and often
superior to traditional methods. In this sense, we put
wavelets in action.",
}
@Article{haa:haar,
title = "Zur {T}heorie der orthogonalen {F}unktionensysteme",
author = "Alfred Haar",
journal = "Mathematische Annalen",
volume = "69",
pages = "331--371",
year = "1910",
note = "In German",
}
@Article{hal-ker-pic:block,
title = "Block threshold rules for curve estimation using
kernel and wavelet methods",
author = "Hall, P. and Kerkyacharian, G. and Picard, D.",
journal = AofS,
volume = "26",
number = "3",
year = "1998",
pages = "922--942",
keywords = "adaptivity bias convergence rate density estimation
minimax nonparametric regression smoothing parameter
variance",
abstract = "Motivated by recently developed threshold rules for
wavelet estimators, we suggest threshold methods for
general kernel density estimators, including those
of classical Rosenblatt-Parzen type. Thresholding
makes kernel methods competitive in terms of their
adaptivity to a wide variety of aberrations in
complex signals. It is argued that term-by-term
thresholding does not always produce optimal
performance, since individual coefficients cannot be
estimated sufficiently accurately for reliable
decisions to be made. Therefore, we suggest grouping
coefficients into blocks and making simultaneous
threshold decisions about all coefficients within a
given block. It is argued that block thresholding
has a number of advantages, including that it
produces adaptive estimators which achieve
minimax-optimal convergence rates without the
logarithmic penalty that is sometimes associated
with term-by-term thresholding. More than this, the
convergence rates are achieved over large classes of
functions with discontinuities, indeed with a number
of discontinuities that diverges polynomially fast
with sample size. These results are also established
for block thresholded wavelet estimators, which,
although they can be interpreted within the kernel
framework, are often most conveniently constructed
in a slightly different way.",
}
@Article{hal-ker-pic:minimax,
title = "On the minimax optimality of block thresholded
wavelet estimators",
author = "Hall, P. and Kerkyacharian, G. and Picard, D.",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "33--49",
keywords = "Besov space. chirp function. convergence
rate. Doppler function. mean squared
error. nonparametric regression. smoothing
parameter",
abstract = "Block thresholding methods have been proposed by
Hall, Kerkyacharian and Picard (1995) as a means of
obtaining increased adaptivity when estimating a
function using wavelet methods. For example, it has
been shown that block thresholding reduces mean
squared error by rendering the estimator more
adaptive to relatively subtle, local changes in
curvature, of the type that local bandwidth choice
is designed to accommodate in traditional kernel
methods. In this paper we show that block
thresholding also provides extensive adaptivity to
many varieties of aberration, including those of
chirp and Doppler type. Indeed, in a wide variety of
function classes, block thresholding methods possess
minimax-optimal convergence rates, and in particular
enjoy those rates without the extraneous logarithmic
penalties that are usually suffered by term-by-term
thresholding methods.",
}
@Article{hal-mck-tur:performance,
title = "Performance of wavelet methods for functions with many
discontinuities",
author = "Peter Hall and Ian McKay and Berwin Turlach",
journal = AofS,
volume = "24",
number = "6",
year = "1996",
pages = "???--???",
abstract = "",
}
@TechReport{hal-nas:non-integer,
title = "On Choosing a Non-integer Resolution Level when Using
Wavelet Methods",
author = "Peter Hall and Guy P. Nason",
year = "1996",
institution = "Centre for Mathematics and its Applications,
Australian National University",
}
@Article{hal-pat:effect,
title = "Effect of Thresholding Rules on Performance of
Wavelet-Based Curve Estimators",
author = "Peter Hall and Prakash Patil",
journal = SSin,
volume = "6",
year = "1996",
pages = "331--345",
abstract = "",
}
@Article{hal-pat:methods,
title = "On wavelet methods for estimating smooth functions",
author = "Peter Hall and Prakash Patil",
journal = Ber,
volume = "1",
number = "1",
year = "1995",
pages = "41--58",
abstract = "Without assuming any prior knowledge of wavelet
methods, we develop theory describing their performance
as estimators of smooth functions. The linear part of
the wavelet estimator is discussed by analogy with
classical kernel methods. Concise formulae are
developed for its bias, variance and mean square error.
These quantities oscillate somewhat erratically on a
wavelength that is equivalent to the bandwidth,
reflecting the irregular numerical fluctuations that
are observed in practice. Nevertheless, the
contributions of these oscillations to mean integrated
square error tend to dampen one another out, even over
very small intervals, with the result that mean
integrated square error properties of linear wavelet
methods are much closer to those of kernel methods than
is perhaps reasonable, given the local behaviour. We
illustrate the adaptive qualities of the nonlinear
component of a wavelet estimator by describing its
performance when the target function is smooth but has
high-frequency oscillations. It is shown that the
nonlinear component automatically adapts to changing
local conditions, to the extent of achieving (except
for a logarithmic factor) the same convergence rate as
the optimal linear estimator, but without a need to
adjust the underlying bandwidth. This makes explicitly
clear the way in which the linear part of the estimator
takes care of the ‘average’ characteristics
of the unknown curve, while the nonlinear part corrects
for more erratic fluctuations, in a manner which is
virtually independent of the construction of the linear
part.",
keywords = "convergence rate density estimation differentiability
dilation equation kernel method nonparametric curve
estimation orthogonal series regression scaling
function smoothness wavelet",
}
@Article{hal-pat:smoothing,
journal = JRSSB,
volume = "58",
number = "2",
year = "1996",
pages = "361--377",
title = "{O}n the choice of smoothing parameter, threshold and
truncation in nonparametric regression by non-linear
wavelet methods",
author = "P. Hall and P. Patil",
abstract = "Concise asymptotic theory is developed for non-linear
wavelet estimators of regression means, in the context
of general error distributions, general designs,
general normalizations in the case of stochastic
design, and non-structural assumptions about the mean.
The influence of the tail weight of the error
distribution is addressed in the setting of choosing
threshold and truncation parameters. Mainly, the tail
weight is described in an extremely simple way, by a
moment condition; previous work on this topic has
generally imposed the much more stringent assumption
that the error distribution be normal. Different
approaches to correction for stochastic design are
suggested. These include conventional kernel estimation
of the design density, in which case the interaction
between the smoothing parameters of the non-linear
wavelet estimator and the linear kernel method is
described.",
}
@Article{hal-pen-ker-pic:block,
journal = SC,
volume = "7",
number = "2",
year = "1997",
pages = "115--124",
title = "Numerical performance of block thresholded wavelet
estimators",
author = "Peter Hall and Spiridon Penev and G{\'e}rard
Kerkyacharian and Dominique Picard",
keywords = "Adaptivity bias density estimation mean squared error
non-parametric regression smoothing parameter
variance",
abstract = "Usually, methods for thresholding wavelet estimators
are implemented term by term, with empirical
coefficients included or excluded depending on whether
their absolute values exceed a level that reflects
plausible moderate deviations of the noise. We argue
that performance may be improved by pooling
coefficients into groups and thresholding them
together. This procedure exploits the information that
coefficients convey about the sizes of their
neighbours. In the present paper we show that in the
context of moderate to low signal-to-noise ratios, this
`block thresholding' approach does indeed improve
performance, by allowing greater adaptivity and
reducing mean squared error. Block thresholded
estimators are less biased than term-by-term
thresholded ones, and so react more rapidly to sudden
changes in the frequency of the underlying signal. They
also suffer less from spurious aberrations of Gibbs
type, produced by excessive bias. On the other hand,
they are more susceptible to spurious features produced
by noise, and are more sensitive to selection of the
truncation parameter.",
}
@TechReport{hal-tur:competitors,
title = "Convolution and Interpolation: {C}ompetitors with
Local Polynomial Smoothing",
author = "Peter Hall and Berwin A. Turlach",
institution = "Centre for Mathematics and its Applications,
Australian National University",
number = "SRR95-037",
year = "1995",
email = "berwin@alphasun.anu.edu.au",
abstract = "Local polynomial smoothing enjoys a variety of very
attractive features. It is often viewed as superior to
convolution and interpolation methods, which offer
greater numerical stability but inferior theoretical
performance. In this paper we show that modifications
to convolution and interpolation techniques produce
effective competitors with local polynomial smoothing,
enjoying similar bias, variance and mean squared error
properties but without the downside of numerical
instability. The methods suggested here may be employed
as the basis for empirical wavelet transforms of
ungridded data.",
}
@Article{hal-tur:enhancing,
title = "Enhancing Convolution and Interpolation Methods for
Nonparametric Regression",
author = "Peter Hall and Berwin A. Turlach",
journal = BKA,
volume = "84",
number = "4",
year = "1997",
pages = "779--790",
email = "halstat@fac.anu.edu.au,berwin.turlach@anu.edu.au",
}
@Book{har-etal:wavelets,
title = "Wavelets, Approximation, and Statisticsl
Applications",
author = "Wolfgang H{\"a}rdle and Gerard Kerkyacharian and
Dominique Picard and Alexander Tsybokov",
booktitle = "Wavelets, Approximation, and Statisticsl
Applications",
series = "Lecture Notes in Statistics",
volume = "129",
publisher = "Springer-Verlag",
address = "New York",
pages = "265",
year = "1998",
}
@Article{hen-etal:invest,
title = "Investigating the Nonlinear Dynamics of Cellular
Motion in the Inner Ear Using the Short-Time {F}ourier
and Continuous Wavelet Transforms",
author = "Conor Heneghan and Shyam Khanna and {\AA}ke Flock and
Mats Ulfendahl and Lou Brundin and Malvin C. Teich",
journal = IEEETSP,
volume = "42",
number = "12",
year = "1994",
pages = "3335--3352",
abstract = "The short-time Fourier transform (STFT) and the
continuous wavelet transform (CWT) are used to analyze
the time course of cellular motion in the inner ear.
The velocity responses of individual outer hair cells
and Hensen's cells to sinusoidal and amplitude
modulated (AM) acoustical signals applied at the ear
canal display characteristics typical of nonlinear
systems, including the generation of harmonic and
half-harmonic components. The STFT proves to be
valuable for following the time course of the frequency
components generated using sinusoidal and ARM input
signals. The CWT is also useful for analyzing these
signals; however, it is generally not as effective as
the STFT when octave-band-based CWT's are used. For the
transient response, the spectrogram (which is the
squared magnitude of the STFT) and the
octave-band-based scalogram (which is the squared
magnitude of the CWT) prove equally valuable, and the
authors have used both to study the responses of these
cells to step-onset tones of different frequencies.
Such analyses reveal information about the preferred
vibration frequencies of cells in the inner ear and are
useful for deciding among alternative mathematical
models of nonlinear cellular dynamics. A modified
Duffing oscillator model yields results that bear some
similarity to the data.",
}
@Article{her-vet:time-varying,
title = "Orthogonal Time-Varying Filter Banks and Wavelet
Packets",
author = "Cormac Herley and Martin Vetterli",
journal = IEEETSP,
volume = "42",
number = "10",
year = "1994",
pages = "2650--2663",
}
@Book{her-wei:first,
title = "A First Course on Wavelets",
author = "Eugenio Hern\'{a}ndez and Guido Weiss",
publisher = "CRC Press Inc.",
address = "Boca Raton",
pages = "512",
year = "1996",
URL = "http://www.crcpress.com/prods/8274.htm",
abstract = "Wavelet theory had its origin in quantum field theory,
signal analysis, and function space theory. In these
areas wavelet-like algorithms replace the classical
Fourier-type expansion of a function. This unique new
book is an excellent introduction to the basic
properties of wavelets, from background math to
powerful applications. The authors provide elementary
methods for constructing wavelets, and illustrate
several new classes of wavelets. The text begins with a
description of local sine and cosine bases that have
been shown to be very effective in applications. Very
little mathematical background is needed to follow this
material. A complete treatment of band-limited wavelets
follows. These are characterized by some elementary
equations, allowing the authors to introduce many new
wavelets. Next, the idea of multiresolution analysis
(MRA) is developed, and the authors include simplified
presentations of previous studies, particularly for
compactly supported wavelets. Some of the topics
treated include: Several bases generated by a single
function via translations and dilations;
Multiresolution analysis, compactly supported wavelets,
and spline wavelets; Band-limited wavelets;
Unconditionality of wavelet bases; Characterizations of
many of the principal objects in the theory of
wavelets, such as low-pass filters and scaling
functions. The authors also present the basic
philosophy that all orthonormal wavelets are completely
characterized by two simple equations, and that most
properties and constructions of wavelets can be
developed using these two equations. Material related
to applications is provided, and constructions of
splines wavelets are presented. Mathematicians,
engineers, physicists, and anyone with a mathematical
background will find this to be an important text for
furthering their studies on wavelets.",
}
@Article{her:boundary,
title = "Boundary Filters for Finite-Length Signals and
Time-Varying Fitler Banks",
author = "Cormac Herley",
journal = IEEETCS2,
volume = "42",
number = "2",
year = "1995",
pages = "102--114",
}
@Article{hes-wic:wavelets,
title = "Wavelets and time-frequency analysis",
author = "Nikolaj Hess-Nielsen and Mladen Victor Wickerhauser",
journal = PIEEE,
volume = "84",
number = "4",
year = "1996",
pages = "523--540",
keywords = "time-frequency analysis, wavelet packet analysis,
wavelet analysis, numerical algorithms, continuous
models, frequency spreading control, high frequencies,
nonstationary filtering, periodic wavelet packets, time
localization, linear phase filters, signal
decomposition",
abstract = "We present a selective overview of time-frequency
analysis and some of its key problems. In particular we
motivate the introduction of wavelet and wavelet packet
analysis. Different types of decompositions of an
idealized time-frequency plane provide the basis for
understanding the performance of the numerical
algorithms and their corresponding interpretations
within the continuous models. As examples we show how
to control the frequency spreading of wavelet packets
at high frequencies using nonstationary filtering and
study some properties of periodic wavelet packets.
Furthermore we derive a formula to compute the time
localization of a wavelet packet from its indexes which
is exact for linear phase filters, and show how this
estimate deteriorates with deviation from linear
phase.",
}
@Article{hic-dat:fractal,
title = "Estimation of fractal signals using wavelets and
filter banks",
author = "Hirchoren, G. A. and DAttellis, C. E.",
journal = IEEETSP,
volume = "46",
number = "6",
year = "1998",
pages = "1624--1630",
keywords = "filter banks fractal signals 1/f processes wavelets",
abstract = "A filter bank design based on orthonormal wavelets
and equipped with a multiscale Wiener filter mas
recently proposed for signal restoration and for signal
smoothing of 1/f family of fractal signals corrupted by
external noise. The conclusions obtained in these papers
are based on the following simplificative hypotheses:
1) The wavelet transformation is a whitening filter, and
2) the approximation term of the wavelet expansion can be
avoided when the number of octaves in the multiresolution
analysis is large enough. In this paper, we shelf that the
estimation of 1/f processes in noise can be improved
avoiding these two hypotheses. Explicit expressions of
the mean-square error are given, and numerical comparisons
with previous results are shown.",
}
@InCollection{hil-etal:mri,
title = "Wavelet denoising of functional {MRI} Data",
author = "M. Hilton and Ogden T. and D. Hattery and G. Jawerth
and B. Eden",
pages = "93--114",
crossref = "ald-uns:medicine",
URL = "",
abstract = "",
}
@Article{hir-dat:estimation,
title = "Estimation of Fractal Signals Using Wavelets and
Filter Banks",
author = "Hirchoren, G. A. and {D'Attellis}, C. E.",
journal = IEEETSP,
volume = "46",
number = "6",
year = "1998",
pages = "1624--1630",
}
@InCollection{hol-etal:real-time,
title = "A Real-Time Algorithm for Signal Analysis with the
Help of the Wavelet Transform",
author = "M. Holschneider and R. Kronland-Martinet and J. Morlet
and Ph. Tchamitchian",
pages = "286--297",
crossref = "com-gro-tch:wavelets",
abstract = "",
}
@InCollection{hon:bridges,
title = "Wavelets, probability and statistics: some bridges",
author = "C. Hondr{\'e}",
pages = "",
crossref = "ben-fra:wavelets",
abstract = "",
note = "",
}
@Article{how-per:wavelet,
title = "Wavelet variance, {A}llan variance, and leakage",
author = "David A. Howe and Donald B. Percival",
journal = IEEETIM,
volume = "44",
number = "2",
year = "1995",
pages = "94--97",
URL = "http://weber.u.washington.edu/~dbp/PSFILES/wvavleak.ps.Z",
keywords = "Analysis of variance; Atomic clocks; Frequency
stability; Power-law processes",
abstract = "Wavelets have recently been a subject of great
interest in geophysics, mathematics and signal
processing. The discrete wavelet transform can be used
to decompose a time series with respect to a set of
basis functions, each one of which is associated with a
particular scale. The properties of a time series at
different scales can then be summarized by the wavelet
variance, which decomposes the variance of a time
series on a scale by scale basis. The wavelet variance
corresponding to some of the recently discovered
wavelets can provide a more accurate conversion between
the time and frequency domains than can be accomplished
using the Allan variance. This increase in accuracy is
due to the fat that these wavelet variances give better
protection against leakage than does the Allan
variance.",
}
@Article{hoy-sch:sunspot,
title = "Group Sunspot Numbers: {A} New Solar Activity
Reconstruction",
author = "Douglas V. Hoyt and Kenneth H. Schatten",
journal = "Solar Physics",
volume = "181",
number = "",
year = "1998",
pages = "491--512",
keywords = "",
abstract = "",
}
@Unpublished{hua-cre:deterministic,
title = "Deterministic/Stochastic Wavelet Decomposition for
Recovery of Signal from Noise Data",
author = "Hsin-Cheng Huang and Noel Cressie",
year = "1999",
note = "Submitted to {\em Technometrics}",
}
@InCollection{hua-cre:empirical,
title = "Empirical {B}ayesian spatial prediction using
wavelets",
authors = "Hsin-Cheng Huang and Noel Cressie",
crossref = "mul-vid:biwbm",
pages = "203--222",
URL = "http://wagner.stat.sinica.edu.tw/~hchuang/decomp.ps",
}
@Article{hua:density,
title = "Density estimation by wavelet-based reproducing
kernels",
author = "S. Y. Huang",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "137--151",
keywords = "asymptotics Bernoulli numbers Bernoulli polynomials
density estimation efficiency multiresolution
approximation projection kernel reproducing kernel
reproducing kernel Hilbert space wavelets",
abstract = "Density estimation by wavelet-based reproducing
kernels is studied. Asymptotic bias and variance are
derived. Estimators using spline- wavelets and
Daubechies wavelets are presented as
examples. Kernel order and kernel efficiency are
also discussed. By an integral property of the bias
and an idea from Scott's averaged shifted
histograms, a bias reduction technique based on a
grid point average is proposed. This bias reduction
technique is shown to be variance stable.",
}
@Article{hua:projection,
title = "Projection estimation in multiple regression with
application to functional ANOVA models",
author = "Huang, J.-H. Z.",
journal = AofS,
volume = "26",
number = "1",
year = "1998",
pages = "242--272",
keywords = "ANOVA curse of dimensionality finite elements
interaction least squares polynomials rate of
convergence regression splines tensor product
trigonometric polynomials wavelets",
abstract = "A general theory on rates of convergence of the
least-squares projection estimate in multiple
regression is developed. The theory is applied to
the functional ANOVA model, where the multivariate
regression function is modeled as a specified sum of
a constant term, main effects (functions of one
variable) and selected interaction terms (functions
of two or more variables). The least-squares
projection is onto an approximating space
constructed from arbitrary linear spaces of
functions and their tensor products respecting the
assumed ANOVA structure of the regression
function. The linear spaces that serve as building
blocks can be any of the ones commonly used in
practice: polynomials, trigonometric polynomials,
splines, wavelets and finite elements. The rate of
convergence result that is obtained reinforces the
intuition that low-order ANOVA modeling can achieve
dimension reduction and thus overcome the curse of
dimensionality. Moreover, the components of the
projection estimate in an appropriately defined
ANOVA decomposition provide consistent estimates of
the corresponding components of the regression
function. When the regression function does not
satisfy the assumed ANOVA form, the projection
estimate converges to its best approximation of that
form.",
}
@Book{hub:world,
title = "The World According to Wavelets: The Story of a
Mathematical Technique in the Making",
author = "Barbara Burke Hubbard",
year = "1996",
publisher = "A K Peters",
address = "Wellesley, Massachusetts",
ISBN = "1-56881-047-4",
abstract = "This book, lovingly written and highly accessible,
embraces the often unheralded notion that
mathematics contains ideas that can, and deserve, to
be communicated to a wider public p; even if
what is communicated is at the level of appreciation
rather than practical knowledge. Put simply, it is a
book about the wavelet transform, that strange and
scientifically intriguing new method of encoding
information with an abundance of practical
applications. This book is a wonderfully successful
attempt to entice the non-mathematical reader into
formerly uncharted territory without sacrificing
precision. The material is masterfully organized so
mathematical details can be assimilated at one's own
pace; the main text is devoid of formulas and
relates a story of people and ideas, while separate
boxes and appendices contain intricate discussions
for the more mathematically adventurous. This book
is a rarity in mathematics books in that it
recognizes that both mathematicians and readers
interested in mathematics have a human side.",
}
@Article{hud-fri-may:atmospheric,
title = "Wavelet Transforms and Atmospheric Turbulence",
author = "Lonnie Hudgins and Carl. A. Friehe and Meinhard
E. Mayer",
journal = PRL,
volume = "71",
number = "20",
year = "1993",
pages = "3279--3282",
abstract = "Wavelet cross spectra and cross scalograms are used
to analyze the time-scale structure of bivariate
turbulence data from the boundary layer over the
ocean. The cross scalogram for the streamwise and
vertical turbulent velocity components shows a
highly intermittent pattern with significant
contributions of opposite signs appearing at two
specific scales, approximately 60 m and
approximately 2 km, believed to be related to small-
scale turbulent mixing and large-scale secondary
flow in the boundary layer.",
}
@InCollection{hud-fri-may:fourier,
title = "Fourier and wavelet analysis of atmospheric
turbulence",
author = "Lonnie Hudgins and Carl. A. Friehe and Meinhard
E. Mayer",
pages = "491--498",
crossref = "mey-roq:progress",
}
@Article{hud-hua:bivariate,
title = "Bivariate wavelet analysis of {A}sia monsoon and
{ENSO}",
author = "Lonnie Hudgins and Jianping Huang",
journal = "Advances in Atmospheric Sciences",
volume = "13",
number = "",
year = "1996",
pages = "",
URL = "http://www.eurandom.tue.nl/whitcher/other_papers/hud0hua96.pdf",
abstract = "",
}
@PhdThesis{hud:thesis,
title = "Wavelet Analysis of Atmospheric Turbulence",
author = "Lonnie H. Hudgins",
school = "University of California, Irvine",
year = "1992",
email = "lonnie@lynx.ps.uci.edu",
}
@Article{hwa:estimation,
title = "Estimation of fractional Brownian motion embedded in
a noisy environment using nonorthogonal wavelets",
author = "Hwang, W. L.",
journal = IEEETSP,
volume = "47",
number = "8",
year = "1999",
pages = "2211--2219",
abstract = "We show that nonorthogonal wavelets can characterize
the fractional Brownian motion (fBm) that is in
white noise. We demonstrate the point that
discriminating the parameter of an fBm from that of
noise is equivalent to discriminating the composite
singularity formed by superimposing a peak
singularity on a Dirac singularity. We characterize
the composite singularity by formalizing this
problem as a nonlinear optimization problem, This
yields our parameter estimation algorithm. For
fractal signal estimation, Wiener filtering is
explicitly formulated as a function of the signal
and noise parameters and the wavelets. We show that
the estimated signal is a 1/f process, Comparative
studies through numerical simulations of our methods
with those of Wornell and Oppenheim are presented.",
}
@Article{imh:computing,
title = "Computing the distribution of a quadratic form in
normal variables",
author = "J. P. Imhof",
journal = BKA,
volume = "48",
pages = "419--426",
year = "1961",
}
@Article{iss:product-moment,
title = "On a Formula for the Product-Moment Coefficient of Any
Order of a Normal Frequency Distribution in Any Number
of Variables",
author = "L. Isserlis",
journal = BKA,
volume = "12",
pages = "134--139",
year = "1918",
}
@Article{ist:coefficients,
title = "Wavelet Coefficients of a {G}aussian Process and
Applications",
author = "Jacques Istas",
journal = "Annales de l'Institut Henri Poincare, Section B,
Calcul des Probabilities et Statistique",
volume = "28",
pages = "537--556",
year = "1992",
note = "In French",
keywords = "covariance functions, spectral densities, Gaussian
stationary process, square error, wavelet transform",
abstract = "The author gives the relations between the covariance
functions and the spectral densities of the
approximation and the details of a Gaussian stationary
process at different resolutions. He studies the rate
of convergence of the square error between the process
and its wavelet transform. Then he shows the
convergence in distribution of the projection of the
process to the original process. Finally, proposes a
choice of the regularity of the wavelet in order to
minimize the correlation between the approximation and
the details.",
}
@Article{iya-kuw:earthquake,
title = "Application of wavelets to analysis and simulation
of earthquake motions",
author = "Iyama, J. Kuwamura, H.",
journal = "Earthquake Engineering \& Structural Dynamics",
volume = "28",
number = "3",
pages = "255--272",
year = "1999",
keywords = "wavelet transform simulated earthquake motions
energy input Fourier transform time-frequency
characteristics energy input rate",
abstract = "A method of applying wavelet transform to earthquake
motion analysis is developed from the viewpoint of
energy input structures, in which relationships
between wavelet coefficients and energy input,
namely energy principles in wavelet analysis are
derived. By using the principles, time-frequency
characteristics of the 1995 Hyogoken-Nanbu
earthquake ground motions are analysed and time
histories of energy input for various ranges of
frequencies and epicentral distances are
identified. Furthermore, a technique to simulate
earthquake ground accelerations by wavelet inverse
transform is developed on the condition that target
time-frequency characteristics are
specified. Structural responses to the simulated
accelerations are compared with the target
time-frequency characteristics, which shows
satisfactory correlations between wavelet
coefficients and energy responses in both time and
frequency domains.",
}
@Article{jaw-swe:overview,
author = "B. Jawerth and Wim Sweldens",
title = "An overview of wavelet based multiresolution
analyses",
journal = "SIAM Rev.",
volume = "36",
number = "3",
pages = "377--412",
year = "1994",
URL = "http://cm.bell-labs.com/who/wim/papers/overview.ps",
abstract = "Wavelet-based multiresolution analysis helps in data
compression, operator analysis and developing a
periodic fast wavelet transform algorithm. The analysis
requires definition of a multiresolution analysis and
investigation of the method in which wavelets fit into
the multiresolution analysis. The fitting process
requires a consideration of the semiorthogonal,
orthogonal and biorthogonal wavelets. The application
process requires an understanding of the wavelets on an
interval, wavelet packets, multidimensional waves and
fast wavelet transforms.",
}
@Unpublished{jen-whi:local,
title = "A Semiparametric Wavelet-Based Estimator of a
Locally Stationary Long-Memory Model",
author = "Mark J. Jensen and Brandon Whitcher",
year = "1999",
note = "Under preparation",
}
@Unpublished{jen:alternative,
title = "An Alternative Maximum Likelihood Estimator of
Long-Memeory Processes Using Compactly Supported
Wavelets",
author = "Mark J. Jensen",
journal = JEDC,
volume = "24",
number = "3",
year = "1997",
pages = "361--387",
URL = "http://econwpa.wustl.edu/eprints/em/papers/9709/9709002.abs",
keywords = "ARFIMA, Fractional Integration, Long-memory, MLE,
Wavelets",
abstract = "In this paper we apply compactly supported wavelets
to the ARFIMA(p,d,q) long-memory process to
develop an alternative maximum likelihood estimator
of the differencing parameter, d, that is invariant
to unknown means, model specification, and
contamination. We show that this class of time
series have wavelet transforms whose covariance
matrix is sparse when the wavelet is compactly
supported. It is shown that the sparse covariance
matrix can be approximated to a high level of
precision by a matrix equal to the covariance matrix
except with the off-diagonal elements set equal to
zero. This diagonal matrix is shown to reduce the
order of calculating the likelihood function to an
order smaller than those associated with the exact
MLE method. We test the robustness of the wavelet
MLE of the fractional differencing parameter to a
variety of compactly supported wavelets, series
length, and contamination levels by generating
ARFIMA(p,d,q) processes for different values of
p, d, and q, and calculating the wavelet MLE using
only the main diagonal elements of its covariance
matrix. In our simulations we find the wavelet MLE
to be superior to the approximate frequency MLE when
estimating contaminated ARFIMA(0,d,0), and
uncontaminated ARFIMA(1,d,0) and ARFIMA(0,d,1)
processes except when the MA parameter is close to
one. We also find the wavelet MLE to be robust to
model specification and as such is an attractive
alternative semiparameter estimator to the Geweke,
Porter--Hudak estimator.",
}
@Article{jen:approximate,
title = "An approximate wavelet {MLE} of short and long
memory parameters",
author = "Mark J. Jensen",
journal = SNDE,
volume = "3",
number = "4",
pages = "239--253",
year = "1999",
URL = "http://econwpa.wustl.edu/eprints/em/papers/9802/9802003.abs",
keywords = "Long Memory, Fractional Integration, ARFIMA,
Wavelets",
abstract = "By design a wavelet's strength rests in its ability
to localize a process simultaneously in time-scale
space. The wavelet's ability to localize a time
series in time-scale space directly leads to the
computational efficiency of the wavelet
representation of a N x N matrix operator by
allowing the N largest elements of the wavelet
represented operator to represent the matrix
operator [Devore, et al. (1992a) and (1992b)]. This
property allows many dense matrices to have sparse
representation when transformed by wavelets.In this
paper we generalize the long-memory parameter
estimator of McCoy and Walden (1996) to estimate
simultaneously the short and long-memory
parameters. Using the sparse wavelet representation
of a matrix operator, we are able to approximate an
ARFIMA model's likelihood function with the series'
wavelet coefficients and their
variances. Maximization of this approximate
likelihood function over the short and long-memory
parameter space results in the approximate wavelet
maximum likelihood estimates of the ARFIMA model. By
simultaneously maximizing the likelihood function
over both the short and long-memory parameters and
using only the wavelet coefficient's variances, the
approximate wavelet MLE provides a fast alternative
to the frequency-domain MLE. Furthermore, the
simulation studies found herein reveal the
approximate wavelet MLE to be robust over the
invertible parameter region of the ARFIMA model's
moving average parameter, whereas the
frequency-domain MLE dramatically deteriorates as
the moving average parameter approaches the
boundaries of invertibility.",
}
@Article{jen:ols,
title = "Using wavelets to obtain a consistent ordinary least
squares estimator of the long-memory parameter",
author = "Mark J. Jensen",
journal = JF,
volume = "18",
number = "1",
year = "1999",
pages = "17--32",
email = "jensen@haar.econ.siu.edu",
URL = "http://econwpa.wustl.edu/eprints/em/papers/9710/9710002.abs",
keywords = "fractionally integrated processes long-memory
wavelets",
abstract = "We develop an ordinary least squares estimator of
the long-memory parameter from a fractionally
integrated process that is an alternative to the
Geweke and Porter-Hudak (1983) estimator. Using the
wavelet transform from a fractionally integrated
process, we establish a log-linear relationship
between the wavelet coefficients' variance and the
scaling parameter equal to the log-memory
parameter. This log-linear relationship yields a
consistent ordinary least squares estimator of the
long-memory parameter when the wavelet coefficients'
population variance is replaced by their sample
variance. We derive the small sample bias and
variance of the ordinary least squares estimator and
test it against the GPH estimator and the
McCoy-Walden maximum likelihood wavelet estimator by
conducting a number of Monte Carlo
experiments. Based upon the criterion of choosing
the estimator which minimizes the mean squared
error, the wavelet OLS approach was superior to the
GPH estimator, but inferior to the McCoy-Walden
wavelet estimator for the processes
simulated. However, given the simplicity of
programming and running the wavelet OLS estimator
and its statistical inference of the long-memory
parameter we feel the general practitioner will be
attracted to the wavelet OLS estimator.",
}
@Unpublished{jen:wafip,
title = "Wavelet Analysis of Fractionally Integrated
Processes",
author = "Mark J. Jensen",
year = "1994",
note = "Department of Economics, Washington University",
email = "jensen@wuecona.wustl.edu",
URL = "http://econwpa.wustl.edu/eprints/em/papers/9405/9405001.abs",
keywords = "Long-Memory, Wavelets, Spectral Analysis, 1/f
Processes",
abstract = "In this paper we apply wavelet analysis to the class
of fractionally integrated processes to show that this
class is a member of the $1/f$ family of processes as
defined by Wornell (1993) and to produce an alternative
method of estimating the fractional differencing
parameter. Currently the method by Geweke and
Porter-Hudak (1983) is used most often to estimate and
test the fractional differencing parameter. The GPH
approach, however, has been shown to have poor
statistical properties and suffers from subjective
decisions that the users must make. The wavelet
analysis estimate of the fractional differencing
parameter is shown to be more straightforward and to
provide results that are more robust than the GPH
method.",
}
@Book{joh-kot:book70,
title = "Continuous Univariate Distributions",
booktitle = "Continuous Univariate Distributions",
author = "Norman L. Johnson and Samuel Kotz",
volume = "",
publisher = "Houghton Mifflin",
address = NY,
year = "1970",
}
@Book{joh-kot:book72,
title = "Continuous Multivariate Distributions",
booktitle = "Continuous Multivariate Distributions",
author = "Norman L. Johnson and Samuel Kotz",
volume = "",
publisher = "John Wiley \& Sons, Inc.",
address = NY,
year = "1972",
}
@Article{joh-sil:correlated,
journal = JRSSB,
volume = "59",
number = "2",
year = "1997",
pages = "319--351",
title = "{W}avelet threshold estimators for data with
correlated noise",
author = "I. M. Johnstone and B. W. Silverman",
URL = "http://playfair.Stanford.EDU/reports/johnstone/correl.ps.gz",
abstract = "Wavelet threshold estimators for data with stationary
correlated noise are constructed by applying a
level-dependent soft threshold to the coefficients in
the wavelet transform. A variety of threshold choices
is proposed, including one based on an unbiased
estimate of mean-squared error. The practical
performance of the method is demonstrated on examples,
including data from a neurophysiological context. The
theoretical properties of the estimators are
investigated by comparing them with an ideal but
unattainable 'bench-mark', that can be considered in
the wavelet context as the risk obtained by ideal
spatial adaptivity, and more generally is obtained by
the use of an 'oracle' that provides information that
is not actually available in the data. It is shown that
the level-dependent threshold estimator performs well
relative to the bench-mark risk, and that its minimax
behaviour cannot be improved on in order of magnitude
by any other estimator. The wavelet domain structure of
both short-and long-range dependent noise is
considered, and in both cases it is shown that the
estimators have near optimal behaviour simultaneously
in a wide range of function classes, adapting
automatically to the regularity properties of the
underlying model. The proofs of the main results are
obtained by considering a more general multivariate
normal decision theoretic problem.",
keywords = "decomposition. regression. shrinkage.",
}
@Book{joh-wic:multivariate,
title = "Applied Multivariate Statistical Analysis",
booktitle = "Applied Multivariate Statistical Analysis",
author = "Richard A. Johnson and Dean W. Wichern",
edition = "4",
publisher = "Prentice-Hall, Inc.",
address = "Englewood Cliffs, NJ",
year = "1998",
pages = "799",
}
@Article{joh:adaptivity,
title = "Wavelet shrinkage for correlated data and inverse
problems: {A}daptivity results",
author = "Johnstone, I. M.",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "51--83",
keywords = "adaptation correlated data fractional Brownian
motion linear inverse problems long range dependence
mixing conditions oracle inequalities rates of
convergence unbiased risk estimate wavelet
Vaguelette decomposition wavelet shrinkage wavelet
thresholding",
abstract = "Johnstone and Silverman (1997) described a
level-dependent thresholding method for extracting
signals from correlated noise. The thresholds were
chosen to minimize a data based unbiased risk
criterion. Here we show that in certain asymptotic
models encompassing short and long range dependence,
these methods are simultaneously asymptotically
minimax up to constants over a broad range of Besov
classes. We indicate the extension of the methods
and results to a class of linear inverse problems
possessing a wavelet vaguelette decomposition.",
}
@Article{jon-lon-mai:hurst,
title = "Wavelet packet computation of the {H}urst exponent",
author = "C. L. Jones and G. T. Lonergan and D. E. Mainwaring",
journal = JPA,
volume = "29",
number = "10",
year = "1996",
pages = "2509--2527",
keywords = "signals representations diffusion fractals",
abstract = "Wavelet packet analysis was used to measure the global
scaling behaviour of homogeneous fractal signals from
the slope of decay for discrete wavelet coefficients
belonging to the adapted wavelet best basis. A new
scaling function for the size distribution correlation
between wavelet coefficient energy magnitude and
position in a sorted vector listing is described in
terms of a power law to estimate the Hurst exponent.
Profile irregularity and long-range correlations in
self-affine systems can be identified and indexed with
the Hurst exponent, and synthetic one-dimensional
fractional Brownian motion (fBm) type profiles are used
to illustrate and test the proposed wavelet packet
expansion. We also demonstrate an initial application
to a biological problem concerning the spatial
distribution of local enzyme concentration in fungal
colonies which can be modelled as a self-affine trace
or an `enzyme walk'. The robustness of the wavelet
approach applied to this stochastic system is
presented, and comparison is made between the wavelet
packet method and the root-mean-square roughness and
second-moment approaches for both examples. The wavelet
packet method to estimate the global Hurst exponent
appears to have similar accuracy compared with other
methods, but its main advantage is the extensive choice
of available analysing wavelet filter functions for
characterizing periodic and oscillatory signals.",
}
@InProceedings{kad:choice,
title = "On the Choice of a Wavelet, and the Energy and the
Phase Distributions of the Wavelet Transform",
author = "Shubha Kadambe",
booktitle = "Time-Frequency and Time-Scale Analysis",
organization = IEEESPS,
year = "1992",
pages = "379--382",
address = "Victoria, B.C., Canada",
}
@InProceedings{kai:filtering,
title = "Wavelet filtering in the scale domain",
author = "Gerald Kaiser",
pages = "51--54",
crossref = "szu:wavelet3",
abstract = "It is shown that any convolution operator in the time
domain can be represented exactly as a multiplication
operator in the time-scale (wavelet) domain. The Mellin
transform establishes a one-to-one correspondence
between frequency filters (system or transfer
functions) and scale filters, which are defined as
multiplication operators in the scale domain, subject
to the convergence of the defining integrals.
Applications to the denoising of random signals are
proposed. We argue that the present method is more
suitable for removing the effects of atmospheric
turbulence than the conventional procedures based on
Fourier analysis because it is ideally suited for
resolving spectral power laws.",
}
@Book{kai:friendly,
title = "A Friendly Guide to Wavelets",
author = "Gerald Kaiser",
publisher = "Springer-Verlag",
address = NY,
year = "1994",
pages = "300",
ISBN = "0-8176-3711-7",
keywords = "Suggestions to the Reader. List of Symbols,
Conventions and Transforms. Preliminaries: Background
and Notation. Windowed Fourier Transforms. Continuous
Wavelet Transforms. Generalized Frames: Key to Analysis
and Synthesis. Discrete Time-Frequency Analysis and
Sampling. Discrete Time-Scale Analysis. Multiresolution
Analysis. Daubechies' Orthonormal Wavelet Bases.
Introduction to Wavelet Electromagnetics. Applications
to Radar and Scattering. Wavelet Acoustics",
abstract = "This volume consists of two parts. The first part,
forming chapters 1-8, is designed as a textbook for an
introductory one-semester course on wavelet analysis
and time-frequency analysis aimed at graduate students
or advanced undergraduates in science and engineering.
Each of the first eight chapters ends with a set of
straightforward exercises designed to drive home the
concepts just covered, and the graphics should further
facilitate absorption. The second part, form-ing
chapters 9-11, represents original research and is
written in a more advanced style. This section can be
used as a textbook for a second-semester course or,
when combined with chapters 1 \& 3, as a reference for
an advanced research-level seminar.",
}
@Article{kai:mellin,
title = "Wavelet filtering with the {M}ellin transform",
author = "Gerald Kaiser",
journal = AML,
volume = "9",
number = "5",
year = "1996",
pages = "69--74",
abstract = "It is shown that any convolution operator in the time
domain can be represented exactly as a multiplication
operator in the time-scale (wavelet) domain. The Mellin
transform gives a one-to-one correspondence between
frequency filters (system functions) and scale filters
(multiplication operators in the scale domain), subject
to the convergence of the defining integrals.
Applications to the denoising of random signals are
proposed. It is argued that the present method is more
suitable for removing the effects of atmospheric
turbulence than the conventional procedures because it
is ideally suited for resolving spectral power laws.",
}
@Article{kai:physical,
title = "Physical wavelets and radar: {A} variational approach
to remote sensing",
author = "Gerald Kaiser",
journal = IEEEAPM,
volume = "38",
number = "1",
year = "1996",
pages = "15--24",
abstract = "Physical wavelets are acoustic or electromagnetic
waves, resulting from the emission of a time signal by
a localized acoustic or electromagnetic source moving
along an arbitrary trajectory in space. Thus, they are
localized solutions of the wave equation or Maxwell`s
equations. Under suitable conditions, such wavelets can
be used as ``basis'' functions, to construct general
acoustic or electromagnetic waves. This gives a local
alternative to the construction of such waves in terms
of (nonlocal) plane waves, via Fourier transforms. We
give a brief, self-contained introduction to physical
wavelets, and apply them to remote sensing. We define
the ambiguity functional, generalization of the radar
and sonar ambiguity functions, which applies not only
to wideband signals, but also to targets and radar
platforms executing arbitrary nonlinear motions.",
}
@Article{kap-kuo:fractal,
title = "Fractal Estimation from Noisy Data via Discrete
Fractional Gaussian Noise ({DFGN}) and the Haar Basis",
author = "Lance M. Kaplan and C.-C. Jay Kuo",
journal = IEEETSP,
volume = "41",
number = "12",
year = "1993",
pages = "3554--3562",
abstract = "The authors show that the application of the discrete
wavelet transform (DWT) using the Haar basis to the
increments of fractional Brownian motion (fBm), also
known as discrete fractional Gaussian noise (DFGN),
yields coefficients which are weakly correlated and
have a variance that is exponentially related to scale.
Similar results were derived by Flandrin (1989),
Tewfik, and Kim for a continuous-time fBm going through
a continuous wavelet transform (CWT). The new
theoretical results justify an improvement to a fractal
estimation algorithm recently proposed by Wornell and
Oppenheim. The performance of the new algorithm is
compared with that of Wornell and Oppenheim's (see IEEE
Trans. Signal Processing, vol. 40, p. 611-623, Mar.
1992) algorithm in numerical simulation.",
}
@Article{kar-jon-kni:bias,
title = "Testing for Bias in the Climate Record",
author = "Thomas R. Karl and Philip D. Jones and Richard W.
Knight",
journal = "Science",
volume = "271",
number = "5257",
year = "1996",
pages = "1879--1883",
abstract = "The method climatologists use to calculate trends on
monthly and annual time series do not introduce
significant bias as has been suggested. Perihelion
calender shifts were used to test for bias because they
have no impact on annual mean temperature trends.
Monthly differences were insignificant.",
}
@TechReport{kat-vid-alb:global-local,
author = {Gabriel Katul and Brani Vidakovic and John
Albertson},
title = {Estimating Global and Local Scaling Exponents in
Turbulent Flows using Wavelet Transformations},
institution = {Institute for Statistics and Decision Sciences, Duke
University},
year = {1999},
number = {99-24},
}
@Article{kat-mas:fBm,
title = "On the spectral density of the wavelet transform of
fractional {B}rownian motion",
author = "Takeshi Kato and Elias Masry",
journal = JTSA,
volume = "20",
number = "5",
year = "1999",
pages = "559--563",
}
@Article{kaw-ari:matching,
title = "Signal matching using wavelet correlation",
author = "Kouzou Kawata and Suguru Arimoto",
journal = ECJ3,
volume = "79",
number = "9",
year = "1996",
pages = "23--34",
note = "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
Vol. 78-A, No. 12, December 1995, pp. 1655--1664",
keywords = "wavelet correlation, local correlation, bandpass cross
correlation, corresponding problem, complex filter",
abstract = "The problem of detecting corresponding points is
studied in the case in which local deformations exist
and a new method named ``wavelet correlation'' is
proposed. There is a difficulty in that a reasonable
window width cannot be designed in local correlation,
which is one of the methods for a corresponding
problem. The wavelet correlation is derived by
extending the notion of local correlation and is
considered to overcome difficulty. The fundamental
concept is derived by the belief that a signal can be
decomposed to several (sinusoidal) components and the
window width can be varied according to each component.
It is claimed that any algorithm using local
correlation can be replaced by the one using wavelet
correlation. In this paper, the wavelet correlation
derived from local correlation is compared with the
Laplacian distance and the local correlation itself by
experiments. Further, a matching method that uses a
narrow-band property of a wavelet correlation function
is proposed and the matching error is evaluated through
experiments using one-dimensional signals. Finally, an
absolute measure of matching by using normalized
wavelet correlation is introduced and applied for
detecting discontinuities of local deformations.",
}
@Article{ken-woo:fractal,
title = "Estimating the fractal dimension of a locally
self-similar {G}aussian process by using increments",
author = "J. T. Kent and A. T. A. Wood",
journal = JRSSB,
volume = "59",
number = "3",
year = "1997",
pages = "679--700",
}
@Article{ker-pic-tri:lp,
title = "Lp adaptive density estimation",
author = "G{\'e}rard Kerkyacharian and Dominique Picard and
Karine Tribouley",
journal = Ber,
volume = "2",
number = "3",
year = "1996",
pages = "229--247",
URL = "",
abstract = "We provide global adaptive wavelet-type density
estimates. Our procedures illustrate the refinement
which can be obtained by replacing the Fourier basis by
the wavelet basis in estimation methods. The main
argument consists in observing that the estimated total
energy of the details of a specified level j will be
smaller or greater than some known threshold if
precisely j is above or below the theoretical optimal
level calculated with the a priori knowledge of the
regularity of the density. This balancing effect leads
directly to an adaptation procedure, and some natural
extensions. We investigate the minimax properties of
these procedures and explain their evolution for
different global error measures.",
keywords = "adaptive estimation Besov spaces density estimation
minimax estimation U-estimate wavelet orthonormal
bases",
}
@Article{kes-mou:matching,
title = "Matching wavelet packets to Gaussian random
processes",
author = "Keshava, N. and Moura, J. M. F.",
journal = IEEETSP,
volume = "47",
number = "6",
year = "1999",
pages = "1604--1614",
keywords = "basis functions best basis search Bhattacharyya
coefficient binary detection classification
nonadditive cost function random processes wavelet
packet",
abstract = "In this paper, we consider the problem of
approximating a set of arbitrary, discrete-time,
Gaussian random processes by a single,
representative wavelet-based, Gaussian process. We
measure the similarity between the original
processes and the wavelet-based process with the
Bhattacharyya coefficient, By manipulating the
Bhattacharyya coefficient, we reduce the task of
defining the representative process to finding an
optimal unitary matrix of wavelet-based
eigenvectors, an associated diagonal matrix of
eigenvalues, and a mean vector. The matching
algorithm we derive maximizes the nonadditive
Bhattacharyya coefficient in three steps: a
migration algorithm that determines the best basis
by searching through a wavelet packet tree for the
optimal unitary matrix of wavelet-based
eigenvectors; and two separate fixed-point
algorithms that derive an appropriate set of
eigenvalues and a mean vector. We illustrate the
method with two different classes of processes:
first-order Markov and bandlimited, The technique is
also applied to the problem of robust terrain
classification in polarimetric SAR images.",
}
@Article{kha-duc:detection,
title = "Detection and classification of multiple events in
piecewise stationary signals: {C}omparison between
autoregressive and multiscale approaches",
author = "Khalil, M. and Duch{\^e}ne, J.",
journal = SP,
volume = "75",
number = "3",
year = "1999",
pages = "239--251",
email = "mohamad.khalil@univ-troyes.fr",
URL = "http://www.elsevier.nl/cas/tree/store/sigpro/sub/1999/75/3/1382.pdf",
keywords = "detection classification rejection wavelet AR
modelling multiscale decomposition",
abstract = "In this paper, we present methods of detection and
classification of events in nonstationary signals
which are well adapted to uterine EMG
processing. Two sequential methods of detection are
presented: the first one is monodimensional and
based on AR modelling, the second is
multidimensional and achieved by decomposing the
signal onto scales using wavelet
transform. Hypothesis rejection is achieved using
either AR coefficients or a variance covariance
matrix computed from the scales. Both methods are
adaptive and allow event detection without
necessarily returning to the null hypothesis
H-o. They have been applied to simulated data and
uterine EMG. Their performances have been compared
together.",
}
@InCollection{kol:application,
title = "An application of wavelet shrinkage to tomography",
author = "Eric D. Kolaczyk",
pages = "77--92",
crossref = "ald-uns:medicine",
URL = "",
abstract = "",
}
@Article{kol:burst,
title = "Non-Parametric Estimation of Gamma-Ray Burst
Intensities Using Haar Wavelets",
author = "Eric D. Kolaczyk",
journal = ApJ,
volume = "483",
number = "1",
year = "1997",
pages = "340--349",
URL = "ftp://galton.uchicago.edu/pub/kolaczyk/TIPSH_Appl.ps.Z",
abstract = "In this article, I present a method for the
non-parametric (model-free) estimation of intensity
profiles underlying gamma-ray bursts. The method,
TIPSH, is based on applying specially calibrated
thresholds to the Haar wavelet coefficients of binned
counts gathered from such bursts. As functions
well-localized with respect to both time and scale,
wavelets are an ideal tool for working with the often
sharp, abrupt nature of gamma-ray burst signals. When
applied to an idealized signal in a small simulation
study and a selection of actual gamma-ray bursts, the
TIPSH algorithm is found to be well capable of
simultaneously estimating the smooth, uniform
background and the pulse-like structure of gamma-ray
burst signals.",
}
@Article{kol:method,
title = "Wavelet shrinkage estimation of certain Poisson
intensity signals using corrected thresholds",
author = "Eric D. Kolaczyk",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "119--135",
URL = "ftp://galton.uchicago.edu/pub/kolaczyk/PoisTholds.ps.Z",
keywords = "gamma-ray bursts. large deviations. Poisson
processes. wavelets",
abstract = "Wavelet shrinkage estimation has been found to be a
powerful tool for the non-parametric estimation of
spatially variable phenomena. Most work in this area
to date has concentrated primarily on the use of
wavelet shrinkage techniques in contexts where the
data are modeled as observations of a signal plus
additive, Gaussian noise. In this paper, I introduce
an approach to estimating intensity functions for a
certain class of ``burst-like'' Poisson processes
using wavelet shrinkage. The proposed method is
based on the shrinkage of wavelet coefficients of
the original count data, as opposed to the current
approach of pre-processing the data using Anscombe's
square root transform and working with the resulting
data in a Gaussian framework. ``Corrected'' versions
of the usual Gaussian-based shrinkage thresholds are
used. The corrections explicitly account for effects
of the first few cumulants of the Poisson
distribution on the tails of the coefficient
distributions. A large deviations argument is used
to justify these corrections. The performance of the
new method is examined, and compared to that of the
pre-processing approach, in the context of an
application to an astronomical gamma-ray burst
signal.",
}
@Unpublished{kol:poisson,
title = "Estimation of Intensities of Burst-Like Poisson
Processes Using Haar Wavelets",
author = "Eric D. Kolaczyk",
note = "Submitted to the {\em Journal of the Royal Statistical
Society, Series B}",
year = "1997",
URL = "ftp://galton.uchicago.edu/pub/kolaczyk/TIPSH_Mod.ps.Z",
abstract = "I present a method for producing estimates of the
intensity function of certain `burst-like'
inhomogeneous Poisson processes, based on the shrinkage
of Haar wavelet coefficients of the observed counts.
The Haar basis is a natural wavelet basis in which to
work in this context, and I derive thresholds for
shrinkage estimation based on the distribution of the
coefficients. The translation-invariant de-noising
approach of Donoho and Coifman (1995) is used in
conjunction with these level-dependent thresholds to
yield smooth estimates, without the usual `staircase'
structure associated with Haar wavelets. This work is
motivated by recent efforts in astronomy to model the
intensity functions underlying gamma-ray bursts. It is
demonstrated that the method proposed herein (TIPSH)
yields sharper estimates of the detail structure in
these signals than those obtained through an analogous
version of the standard adaptation of wavelet shrinkage
for Poisson counts, based on the square-root
transformation.",
}
@Article{kol:shrinkage,
journal = JASA,
volume = "91",
number = "435",
year = "1996",
pages = "1079--1090",
title = "{A} wavelet shrinkage approach to tomographic image
reconstruction",
author = "E. D. Kolaczyk",
abstract = "A method is proposed for reconstructing images from
tomographic data with respect to a two-dimensional
wavelet basis. The Wavelet-vaguelette decomposition
(WVD) is used as a framework within which expressions
for the necessary wavelet coefficients may be derived.
These coefficients are calculated using a version of
the filtered back-projection algorithm as a
computational tool, in a multiresolution fashion. The
necessary filters are defined in terms of the
underlying wavelets. Denoising is accomplished through
an adaptation of the wavelet shrinkage (WS) approach of
Donoho et al. and amounts to a form of regularization.
Combining these two steps yields the proposed WVD/WS
reconstruction algorithm, which is compared to the
traditional filtered backprojection method in a small
study.",
keywords = "decomposition, backprojection. tomography.
wavelet-vaguelette",
}
@Article{kom-etal:helioseismic,
title = "Multitaper spectral analysis and wavelet denoising
applied to helioseismic data",
author = "Komm, R. W. and Gu, Y. and Hill, F. and Stark,
P. B. and Fodor, I. K.",
journal = ApJ,
volume = "519",
number = "1",
year = "1999",
pages = "407--421",
abstract = "Estimates of solar normal mode frequencies from
helioseismic observations can be improved by using
multitaper spectral analysis (MTSA) to estimate spectra
from the time series, then using wavelet denoising of
the log spectra. MTSA leads to a power spectrum
estimate with reduced variance and better leakage
properties than the conventional periodogram. Under the
assumption of stationarity and mild regularity
conditions, the log multitaper spectrum has a
statistical distribution that is approximately Gaussian,
so wavelet denoising is asymptotically an optimal method
to reduce the noise in the estimated spectra. We find
that a single m-v spectrum benefits greatly from MTSA
followed by wavelet denoising and that wavelet denoising
by itself can be used to improve m-averaged spectra. We
compare estimates using two different five-taper
estimates (Slepian and sine tapers) and the periodogram
estimate for Global Oscillation Network Group (GONG)
time series at selected angular degrees l. We compare
those three spectra with and without wavelet denoising,
both visually and in terms of the mode parameters
estimated from the preprocessed spectra using the GONG
peak-fitting algorithm. The two multitaper estimates
give equivalent results. The number of modes fitted well
by the GONG algorithm is 20%-60% larger (depending on l
and the temporal frequency) when applied to the
multitaper estimates than when applied to the
periodogram. The estimated mode parameters (frequency,
amplitude, and width) are comparable for the three power
spectrum estimates, except for modes with very small
mode widths (a few frequency bins), where the multitaper
spectra broaden the modes compared with the periodogram.
At frequencies below 3 mHz, wavelet denoising of the log
multitaper power spectra tends to increase the number of
modes for which the GONG peak-fitting algorithm
converges well. Close to 3 mHz, where all modes are
resolved, wavelet denoising makes little difference. At
higher frequencies close to the acoustic cutoff
frequency, where modes are blended into ridges, wavelet
denoising the multitaper spectra reduces the number of
good fits. We tested the influence of the number of
tapers used and found that narrow modes at low n-values
are broadened to the extent that they can no longer be
fitted if the number of tapers is too large. For
helioseismic time series of this length and temporal
resolution, the optimal number of tapers is less than
10.",
}
@Book{koo:wavelets,
title = "Wavelets: {A}n Elementary Treatment of Theory and
Applications",
editor = "Tom H. Koornwinder",
series = "Approximations and Decompositions",
volume = "1",
publisher = "World Scientific",
address = "Singapore",
pages = "225",
year = "1993",
keywords = "",
abstract = "",
}
@Book{kot-joh-rea:encyclopedia,
title = "Encyclopedia of Statistical Sciences",
booktitle = "Encyclopedia of Statistical Sciences",
editor = "Samuel Kotz and Norman L. Johnson and Campbell
B. Read",
publisher = "Wiley",
address = NY,
year = "1982",
}
@Article{kov-sil:extending,
title = "Extending the scope of wavelet regression methods by
coefficient-dependent thresholding",
author = "Arne Kovac and Bernard W. Silverman",
journal = JASA,
volume = "95",
number = "449",
year = "2000",
pages = "172--183",
}
@InProceedings{kri-dro-pes:multiscale,
title = "{M}ultiscale detection of nonstationary signals",
booktitle = "Time-Frequency and Time-Scale Analysis",
organization = IEEESPS,
year = "1992",
pages = "105--108",
address = "Victoria, B.C., Canada",
author = "H. Krim and K. Drouiche and J. C. Pesquet",
abstract = "A statistical method for detecting and/or localizing
nonstationarities in a process observed over a time
interval T is presented. Stationarity is induced by
taking a wavelet transform of the process. A
parametric model is fitted to the result. The error
incurred in fitting the model is shown to preserve
the singularity manifested in the transform. The
error is then used to establish a statistical
detection test that is free of any prior knowledge
about the class of signals being analyzed, and of
any user input.",
keywords = "multiscale detection. nonstationary
signals. statistical method. time interval. wavelet
transform. parametric
model. singularity. statistical detection test.",
}
@InProceedings{kri-pes-wil:robust,
title = "{R}obust multiscale representation of processes and
optimal signal reconstruction",
booktitle = "Proceedings of the IEEE-SP International Symposium
on Time-Frequency and Time-Scale Analysis",
pages = "1--4",
year = "1994",
author = "H. Krim and J. C. Pesquet and A. S. Willsky",
note = "25-28 Oct. 1994, Philadelphia, PA, USA",
abstract = "We propose a statistical approach to obtain a ``best
basis'' representation of an observed random
process. We derive statistical properties of a
criterion first proposed to determine the best
wavelet packet basis, and, proceed to use it in
constructing a statistically sound algorithm. For
signal enhancement, this best basis algorithm is
followed by a nonlinear filter based on the minimum
description length (MDL) criterion. We show that it
is equivalent to a min-max based algorithm proposed
by Donoho and Johnstone (1992).",
keywords = "optimal signal reconstruction. statistical
approach. robust multiscale representation. random
process. wavelet packet basis. statistically sound
algorithm. signal enhancement. best basis
algorithm. nonlinear filter. minimum description
length criterion. min-max based algorithm. white
noise. Gaussian noise.",
}
@Article{kri-pes:nonstationary,
title = "Multiresolution analysis of a class of nonstationary
processes",
author = "H. Krim and J. C. Pesquet",
journal = IEEETIT,
volume = "41",
number = "4",
year = "1995",
pages = "1010--1020",
keywords = "multiresolution analysis, nonstationary processes,
signal processing, nonstationary signals, multiscale
framework, discrete-time analysis, parametric model,
wide-sense stationarity, analysis wavelet, wavelet
packet analysis, nonstationarities",
abstract = "Processing nonstationary signals is an important and
challenging problem. We focus on the class of
nonstationary processes with stationary increments of
an arbitrary order, and place them in a multiscale
framework. Unlike other related studies, we concentrate
on the discrete-time analysis and derive a number of
new results in addition to placing the related existing
ones in the same framework. We extend the study to
various parametric models for which we derive the
resulting multiresolution description. We show that
wide-sense stationarity may be achieved by adequately
selecting the analysis wavelet. After generalizing the
study to wavelet packet analysis, we show that the
latter possesses additional properties which are useful
in the presence of other types of nonstationarities.",
}
@Article{kri-etal:denoising,
title = "On denoising and best signal representation",
author = "Krim, H. and Tucker, D. and Mallat, S. and Donoho,
D.",
journal = IEEETIT,
volume = "45",
number = "7",
year = "1999",
pages = "2225--2238",
abstract = "We propose a best basis algorithm for signal
enhancement in white Gaussian noise. The best basis
search is performed in families of orthonormal bases
constructed with wavelet packets or local cosine
bases. We base our search for the ``best'' basis on
a criterion of minimal reconstruction error of the
underlying signal. This approach is intuitively
appealing because the enhanced or estimated signal
has an associated measure of performance, namely,
the resulting mean-square error. Previous approaches
in this framework have focused on obtaining the most
``compact'' signal representations, which
consequently contribute to effective denoising,
These approaches, however, do not possess the
inherent measure of performance which our algorithm
provides. We first propose an estimator of the
mean-square error, based on a heuristic argument and
subsequently compare the reconstruction performance
based upon it to that based on the Stein unbiased
risk estimator. We compare the two proposed
estimators by providing both qualitative and
quantitative analyses of the bias term. Having two
estimators of the mean-square error, we incorporate
these cost functions into the search for the
``best'' basis, and subsequently provide a
substantiating example to demonstrate their
performance.",
}
@Article{kro-ram-jon:frequency-shift-invariant,
title = "Frequency-shift-invariant orthonormal wavelet packet
representations",
author = "Krongold, B. S. and Ramchandran, K. and Jones,
D. L.",
journal = IEEETSP,
volume = "47",
number = "9",
pages = "2579--2582",
abstract = "It is commonly known that the dyadic structure of
wavelet expansions results in both time- and
frequency-translation sensitivity of an input
signal. We develop the first efficient method to
reduce frequency-alignment sensitivity by
introducing a wavelet packet decomposition that is
invariant to frequency shifts of a signal. A
frequency-shifted wavelet packet library is
presented, and an efficient best-basis algorithm is
developed to determine the best signal
representation among all frequency shifts of a
signal. The algorithm computes all frequency-shifted
coefficients in O(N-2) operations, followed by an
efficient depth-first tree search of the same
complexity."
}
@Article{kul-sad-mur:trough,
title = "Wavelet analysis of intermittent turbulent transport
in the atmospheric surface layer over a monsoon
trough region",
author = "Kulkarni, J. R. and Sadani, L. K. and Murthy, B. S.",
journal = BLM,
volume = "90",
number = "2",
year = "1999",
pages = "217--239",
keywords = "atmospheric surface layer quadrant analysis
turbulence intermittency turbulent fluxes wavelet
analysis",
abstract = "The structure of the turbulence in the atmospheric
surface layer over a monsoon trough region has been
studied using structural analysis based on wavelet
transform. The observational site is located at the
eastern (wet) end of the monsoon trough region,
characterized by high moisture in the atmospheric
surface layer. On the average relative humidity
varied from 70% to 100% during the experiment. The
wind and temperature data, collected at Kharagpur
(22 degrees 25' N, 87 degrees 18' E) at six
observational hours of a day in June 1990 during the
Monsoon Trough Boundary Layer Experiment (MONTBLEX),
have been utilized in the study. The wind and
instantaneous momentum flux time series were
decomposed into 12 scales using the Haar wavelet
transform. The eddies exhibited a large temporal
variability generating intermittency in the energy
and Bur distributions. A criterion based on the
isotropy has been suggested for separating the large
eddies from the small eddies. At the separation
scale the isotropy coefficient drops sharply. It is
shown that the intermittency in the small eddies
resulted from the spatial variation of energy, and
deviation of velocity statistics from the Gaussian
distribution known as flatness. The deviation from
the -5/3 power law has been attributed to the
increased mean values of, (i) the coefficient of
variation of energy, and (ii) the flatness factor,
in the inertial subrange. The decomposition of the
instantaneous momentum Bur time series reveals that
the major contribution to the total flux arises from
the large eddies. The quadrant analysis of the
momentum flux shows that ejections and sweeps
account for a substantial part of the total
flux. and quantifies the relative importance of the
various spatial scales that contribute to the
transport of momentum.",
}
@Article{kul:monsoon,
title = "Wavelet analysis of the association between the
{S}outhern {O}scillation and the {I}ndian {S}ummer
{M}onsoon",
author = "Kulkarni, J. R.",
journal = IJC,
volume = "20",
number = "1",
year = "2000",
pages = "89--104",
abstract = "A new aspect of the monsoon-Southern Oscillation
(SO) link has been investigated. All India Summer
Monsoon Rainfall (AISMR) and Southern Oscillation
Index (SOI) data (for August-September-October
months) for the period 1871-1998 have been processed
for wavelet analysis. Using the Haar wavelet
function, the data are decomposed into seven dyadic
scales corresponding to periods of 2, 4, 8, 16, 32,
64 and 128 years. The time frequency localization in
the wavelet analysis was used to study the temporal
variability of modes in AISMR and SOI. The 2 and 8
year modes in both are found to exhibit low
frequency modulation. The 4 year mode in both showed
large intermittency. The periods of high/low
activities of 2, 4 and 8 year modes were associated
with a large/low number of deficient AISMR
years. The SOI derived from 2, 4 and 8 year modes in
the ENSO years, is found to be related to AISMR
variability, at 1% level of significance. The 2, 4
and 8 year modes in AISMR and SOI are found to be
correlated at a 5% level of significance. There is a
large temporal variability in the correlations of
these modes. The occurrences of maxima and minima in
these correlations followed a sequence, first in the
8 year mode, then in the 4 year mode and in the end,
in the 2 year mode. The reasons for de-association
between AISMR activity and SOI in the last 8 years
of the present decade have been attributed to (i)
the negative contributions by 128, 64, 32 and 16
year modes, (ii) the low activity of 4 and 8 year
modes and (iii) the weak correlation between AISMR
and SOI in 4 and 8 year modes during this period.",
}
@InCollection{kum-fou:introduction,
title = "Wavelet analysis in geophysics: {A}n introduction",
author = "Praveen Kumar and Efi Foufoula-Georgiou",
pages = "1--43",
crossref = "fou-kum:geophysics",
keywords = "",
abstract = "",
}
@Article{kum-fou:rainfall,
title = "A New Look at Rainfall Fluctuations and Scaling
Properties of Spatail Rainfall Using Orthogonal
Wavelets",
author = "Praveen Kumar and Efi Foufoula-Georgiou",
journal = JAM,
volume = "32",
year = "1993",
pages = "209--222",
abstract = "Orthogonal wavelet transforms of the rainfall fields
are analyzed. Results show that wavelet multiresolution
analysis provides methods for the study of
nonhomogeneous anisotropic processes and for defining
fluctuations in two dimensions. Moreover, orthogonal
wavelet transforms segregate large-scale features from
small-scale features by providing convenient orthogonal
decompositions with directionality. Lastly, orthogonal
wavelet analysis is applied to a squall-line storm.",
}
@Article{kum-fou:review,
title = "Wavelet analysis for geophysical applications",
author = "Praveen Kumar and Efi Foufoula-Georgiou",
journal = "Review of Geophysics",
volume = "35",
number = "4",
year = "1997",
pages = "385--412",
keywords = "fractional brownian motion 2-scale difference
equations turbulent coherent motions spatial rainfall
fields signal analysis forest canopy multicomponent
decomposition sampling theory transforms
representation",
abstract = "Wavelet transforms originated in geophysics in the
early 1980s for the analysis of seismic signals. Since
then, significant mathematical advances in wavelet
theory have enabled a suite of applications in diverse
fields. In geophysics the power of wavelets for
analysis of nonstationary processes that contain
multiscale features, detection of singularities,
analysis of transient phenomena, fractal and
multifractal processes, and signal compression is now
being exploited for the study of several processes
including space-time precipitation, remotely sensed
hydrologic fluxes, atmospheric turbulence, canopy
cover, land surface topography, seafloor bathymetry,
and ocean wind waves. It is anticipated that in the
near future, significant further advances in
understanding and modeling geophysical processes will
result from the use of wavelet analysis. In this paper
we review the basic properties of wavelets that make
them such an attractive and powerful tool for
geophysical applications, We discuss continuous,
discrete, orthogonal wavelets and wavelet packets and
present applications to geophysical processes.",
}
@Article{kum:role,
title = "Role of Coherent Structures in the Stochastic-Dynamic
Variability of Precipitation",
author = "Praveen Kumar",
journal = JGRA,
volume = "101",
number = "D21",
year = "1996",
pages = "26,393--26,404",
keywords = "spatial rainfall fields, multicomponent decomposition,
wave-propagation, sampling theory, signal",
abstract = "Using time-frequency-scale elements obtained from
wavelet packets as a basis, we describe a broad
framework of analysis which can be used to reveal the
essential dynamics, identified as coherent structures,
of precipitation. We show that the matching pursuits
algorithm with nearly symmetric orthogonal wavelets
provides an optimal representation of the inner
structure of rainfall time series and can describe
features that range from scales of isolated singularity
to synoptically forced large-scale features. We
describe the analysis of time series of several storms
and show that there exist distinct scales of variation
identifiable with rain cell and synoptic-scale
activity, which is in contradistinction to the scale
invariance hypothesis.",
}
@Article{kum:scale-space,
title = "A Wavelet Based Methodology for Scale-Space
Anisotropic Analysis",
author = "Praveen Kumar",
journal = "Geophysical Research Letters",
volume = "22",
number = "20",
year = "1995",
pages = "2777--2780",
abstract = "It is well known that several geophysical fields
exhibit characteristic features at different scales.
For some such fields scale-space anisotropy is also
present, that is, features contributing a significant
fraction of energy are oriented in different directions
at different scales. Examples of such fields include
clouds, rainfall, hurricanes etc. A technique based on
wavelet transforms (with two-dimensional directionally
oriented Morlet wavelet) is developed to analyze such
random fields. This methodology has significant
advantage over Fourier transform based techniques and
is demonstrated using the analysis of a spatial
rainfall field.",
}
@Article{lan-etal:noise,
title = "Noise reduction using an undecimated discrete wavelet
transform",
author = "M. Lang and H. Guo and J. E. Odegard and C. S. Burrus
and R. O. Wells",
journal = IEEESPL,
volume = "3",
number = "1",
year = "1996",
pages = "10--12",
abstract = "A new nonlinear noise reduction method is presented
that uses the discrete wavelet transform. Similar to
Donoho (1995) and Donoho and Johnstone (1994, 1995),
the authors employ thresholding in the wavelet
transform domain but, following a suggestion by
Coifman, they use an undecimated, shift-invariant,
nonorthogonal wavelet transform instead of the usual
orthogonal one. This new approach can be interpreted as
a repeated application of the original Donoho and
Johnstone method for different shifts. The main feature
of the new algorithm is a significantly improved noise
reduction compared to the original wavelet based
approach. This holds for a large class of signals, both
visually and in the l/sub 2/ sense, and is shown
theoretically as well as by experimental results.",
}
@InProceedings{lan-etal:nonlinear,
title = "Nonlinear processing of a shift invariant {DWT} for
noise reduction",
author = "M. Lang and H. Guo and J. E. Odegard and C. S. Burrus
and R. O. Wells",
pages = "640--651",
crossref = "szu:wavelet2",
keywords = "nonlinear processing, shift invariant DWT, noise
reduction, thresholding, redundant wavelet transform,
nondecimated redundant wavelet transform, synthetic
aperture radar, SAR images",
abstract = "A novel approach for noise reduction is presented.
Similar to Donoho, we employ thresholding in some
wavelet transform domain but use a nondecimated and
consequently redundant wavelet transform instead of the
usual orthogonal one. Another difference is the shift
invariance as opposed to the traditional orthogonal
wavelet transform. We show that this new approach can
be interpreted as a repeated application of Donoho`s
original method. The main feature is, however, a
dramatically improved noise reduction compared to
Donoho`s approach, both in terms of the l/sub 2/ error
and visually, for a large class of signals. This is
shown by theoretical and experimental results,
including synthetic aperture radar (SAR) images.",
}
@InProceedings{lar-zak:automatic,
title = "Automatic Classification of Active Sonar Data Using
Time-Frequency Transforms",
author = "Francesco Lari and Avideh Zakhor",
booktitle = "Time-Frequency and Time-Scale Analysis",
organization = IEEESPS,
year = "1992",
pages = "21--24",
address = "Victoria, B.C., Canada",
abstract = "Automatic classification of active sonar signals using
the Wigner-Ville transform (WVT), the wavelet transform
(WT) and the scalogram is addressed. Features are
extracted by integrating over regions in the
time-frequency (TF) distribution, and are classified by
a decision tree. Experimental results show
classification and detection rates of up to 92% at -4
dB of SNR. The WT outperforms the WVT and the
scalogram, particularly at high noise levels. This can
be partially attributed to the absence of cross terms
in the WT.",
}
@Article{lau-wen:climate,
title = "Climate signal detection using wavelet transform:
{H}ow to make a time series sing",
author = "K. M. Lau and Hengyi Weng",
journal = BAMetS,
volume = "76",
number = "12",
pages = "23--41",
year = "1995",
keywords = "",
abstract = "In this paper, the application of the wavelet
transform (WT) to climate time series analyses is
introduced. A tutorial description of the basic
concept of WT, compared with similar concepts used
in music, is also provided. Using an analogy between
WT representation of a time series and a music
score, the authors illustrate the importance of
local versus global information in the
time-frequency localization of climate
signals. Examples of WT applied to climate data
analysis are demonstrated using analytic signals as
well as real climate time series. Results of WT
applied to two climate time series - that is, a
proxy paleoclimate time series with a 2.5-Myr
deep-sea sediment record of [[Delta].sup.18]O and a
140-yr monthly record of Northern Hemisphere surface
temperature - are presented. The former shows the
presence of a 40-kyr and a 100-kyr oscillation and
an abrupt transition in the oscillation regime at
0.7 Myr before the present, consistent with previous
studies. The latter possesses a myriad of
oscillatory modes from interannual (2-5 yr),
interdecadal (10-12 yr, 20-25 yr, and 40-60 yr), and
century ([approximately]180 yr) scales at different
periods of the data record. In spite of the large
difference in timescales, common features in
time-frequency characteristics of these two time
series have been identified. These features suggest
that the variations of the earth's climate are
consistent with those exhibited by a nonlinear
dynamical system under external forcings.",
}
@Article{leb-vet:balanced,
title = "Balanced multiwavelets theory and design",
author = "J{\'e}r{\^o}me Lebrun and Martin Vetterli",
journal = IEEETSP,
volume = "46",
number = "4",
pages = "1119--1125",
year = "1998",
keywords = "balanced multiwavelets time-varying filter banks signal
compression multichannel signal processing multifilter
banks multiwavelets filter bank design multiresolution
analysis",
abstract = "This article deals with multiwavelets, which are a
generalization of wavelets in the context of time-varying
filter banks and with their applications to signal
processing and especially compression. By their inherent
structure, multiwavelets are fit for processing
multichannel signals. This is the main issue in which we
are interested. First, we review material on
multiwavelets and their links with multifilter banks and,
especially, time-varying filter banks. Then, we have a
close look at the problems encountered when using
multiwavelets in applications, and we propose new
solutions for the design of multiwavelets filter banks by
introducing the so-called balanced multiwavelets",
}
@Unpublished{led-muj-mur-smi:motion,
title = "Spatio-Temporal Wavelet Transforms for Motion
Tracking",
author = "Jean-Pierre Leduc and Fernando Mujica and Romain
Murenzi and Mark Smith",
year = "1997",
email = "leduc@ee.gatech.edu",
note = "Georgia Institute of Technology",
}
@Article{led:spatio-temporal,
title = "Spatio-Temporal Wavelet Transforms for Digital Signal
Analysis",
author = "Jean-Pierre Leduc",
journal = SP,
volume = "60",
number = "1",
pages = "23--41",
year = "1997",
email = "leduc@ee.gatech.edu, leduc@irisa.fr",
keywords = "Wavelet transforms; Spatio-temporal signals; Image
seqeunces; Motion analysis; Group of transfromations;
Regions of interest; Selective feature extraction",
abstract = "The goal of this paper is to investigate
spatio-temporal continuous wavelet transforms. A new
wavelet family called the Galilean wavelet has been
designed to tune to four main parameters namely the
scale, the spatio-temporal position, the spatial
orientation, and the velocity. The paper starts with
the theory of motion-compensated wavelet filtering in
the discrete realm of image processing. As a major
difference to multi-dimensional homogeneous spaces, the
spatio-temporal signals involve motions that warp the
signal along the temporal dimension. Modeling motion
with 2-D affine transformations leads to
spatio-temporal generalizations. Decomposition in to
elementary operators lead to developing transformation
groups and exploiting the related representation
theory. The construction of continuous spatio-temporal
wavelets in $R^n \times R$ spaces is then handled with
classical techniques of calculation. Close connections
may then be established among all the spatio-temp oral
wavelet transforms through different sets of
transformations. This approachgenerates a general
framework for the study of future tools. Frames of
wavelets are thereafter investigated to revisit
discrete wavelet transforms in a more general way.
Eventually illustrations demonstrate the ability of the
Galilean wavelet transforms to analyze spatio-temporal
contents.",
}
@TechReport{lee-har-spe:tides,
title = "Automated Smoothing of Tides Data Using Wavelets",
author = "GeungHee Lee and Jeffrey D. Hart and F. Michael
Speed",
institution = "Department of Statistics, Texas A\&M University",
number = "268",
year = "1996",
keywords = "automatic trend, jump, outlier, shrinkage estimator,
wavelet packet",
}
@Article{lee:wavelets,
title = "Wavelets and wavelet estimation: {A} review",
author = "Lee, G. H.",
journal = JETE,
volume = "4",
number = "1",
year = "1998",
pages = "123--157",
abstract = "Wavelets have received a lot of attention in
statistics since Donoho and Johnstone (1994)
introduced wavelet shrinkage estimators, which
include some important ideas--wavelets as a new
local basis, multiresolution analysis and
thresholding. From these ideas, we can reilluminate
the methods and data analyses based on Fourier
series and truncated estimators. In this paper, we
review wavelets, wavelet series estimators, their
model selection methods and their applications in
econometrics and economics.",
}
@Book{leh:tpe,
title = "Theory of Point Estimation",
author = "E. L. Lehmann",
publisher = "Wiley",
address = NY,
pages = "506",
year = "1983",
}
@Book{leh:tsh,
title = "Testing Statistical Hypotheses",
author = "E. L. Lehmann",
publisher = "Wiley",
address = NY,
edition = "2",
pages = "600",
year = "1986",
}
@TechReport{len:denoising,
title = "Denoising not equispaced data with wavelets",
author = "L. Lenarduzzi",
year = "1997",
number = "IAMI 97.1",
institution = "Instituto per le Applicazioni della Matematica e
dell'Informatica",
}
@InProceedings{lew-bur:approximate,
title = "Approximate continuous wavelet transform with an
application to noise reduction",
author = "James M. Lewis and C. Sidney Burrus",
booktitle = "Proceedings of the International Conference on
Acoustics, Speech, and Signal Processing",
pages = "???--???",
year = "1998",
URL = "http://www-dsp.rice.edu/publications/pub/lewi-icassp98.ps.Z",
abstract = "We describe a generalized scale-redundant wavelet
transform which approximates a dense sampling of the
continuous wavelet transform (CWT) in both time and
scale. The dyadic scaling requirement of the usual
wavelet transform is relaxed in favor of an
approximate scaling relationship which in the case
of a Gaussian scaling function is known to be
asymptotically exact and irrational. This scheme
yields an arbitrarily dense sampling of the scale
axis in the limit. Similar behavior is observed for
other scaling functions with no explicit analytic
form. We investigate characteristics of the family
of Lagrange interpolating filters (related to the
Daubechies family of compactly-supported orthonormal
wavelets), and finally present applications of the
transform to denoising and edge detection.",
}
@Article{li-noz:cross-correlation,
journal = "Japanese Society of Mechanical Engineers International
Journal, Series B",
volume = "40",
number = "1",
year = "1997",
pages = "58--66",
title = "{A}pplication of wavelet cross-correlation analysis to
a plane turbulent jet",
author = "Hui Li and Tsutomu Nozaki",
abstract = "A new cross-correlation method, which is called
wavelet cross-correlation analysis and is used to
express the statistical cross-correlation of two
arbitrary signals in terms of scale and time delay, is
proposed and its main properties are presented,
analyzing two test signals, it is shown that wavelet
cross-correlation does not have the limitations of
classical cross-correlation. As a practical application
to fluid mechanics, wavelet cross-correlation is
employed to determine the cross-correlation
relationships between the x-components of the
fluctuation velocities at two points on opposite sides
of the centerline and along the centerline of a plane
turbulent jet in terms of period and time delay. In the
distributions of the wavelet cross-correlation
coefficients, similar structures with various scales
are observed instantaneously, and the period of eddy
and apparent flapping motions can be determined easily
in terms of period and time delay. It is found that the
apparent flapping behavior appears first in region with
an intermediate period. It is also revealed that a
similar structure with a high period consists of
similar structures with a low period, i.e., a large
eddy contains small eddies.",
keywords = "turbulent flow, jet, eddy, coherent structure,
branching structure, mixing layer, wavelet analysis,
wavelet cross-correlation function, wavelet
cross-correlation coefficient, local wavelet
cross-spectrum",
}
@Article{li-ulr:well-log,
title = "Well-log analysis using localized transforms",
author = "Li, X. G. and Ulrych, T. J.",
journal = "Journal of Seismic Exploration",
volume = "8",
number = "3",
year = "1999",
pages = "243--260",
abstract = "The wavelet transform (WT) is used to analyze and
characterize well-logs in location and scale. In the
WT domain, a well-log can be decomposed into
deterministic and statistical components. The
deterministic component consists of smooth WT
coefficients at the largest scale and large WT
coefficients at the rest of the scales. The
remaining coefficients represent the statistical
component which can be modeled as a fractional
Brownian motion (FBM). A well-log is used to
illustrate this decomposition. To test the fractal
model, we have used both 1-D and 2-D wavelet
transforms to simulate FBM processes. These
simulated FBM series look like well-logs, which
verifies the proposed approach. Both orthogonal and
continuous WT's are used for analyzing fractal
parameters of FBM processes. The orthogonal WT is
used to compute a fractal parameter for a particular
time series,and the continuous WT is used to
estimate the time variant fractal parameter.",
}
@Article{li:identification,
title = "The wavelet identification of thresholds and time
delay of threshold autoregressive models",
author = "Li, Y.",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "153--166",
keywords = "thresholds time delay wavelets",
abstract = "In this paper, we consider identification of the
thresholds and time delay of threshold
autoregressive models with p- dependence and an
unknown number of thresholds. By checking p
different empirical wavelets of the data to see
which have significantly large absolute values, the
time delay is identified first. By further checking
the empirical wavelets corresponding to the time
delay across the fine scale levels, the thresholds
and their number are identified. All estimators are
shown to be strongly consistent.",
}
@InProceedings{lia-li-kuo:image,
title = "Image compression with embedded multiwavelet coding",
author = "Kai-Chieh Liang and Jin Li and C.-C. Jay Kuo",
pages = "",
crossref = "szu:wavelet3",
URL = "http://sipi.usc.edu/~lijin/paper/aero96_mwt.ps",
abstract = "",
}
@InProceedings{lia-par:2d,
title = "A two-dimensional translation invariant wavelet
representation and its applications",
author = "Jie Liang and Thomas W. Parks",
booktitle = "Proceedings ICIP-94",
volume = "1",
pages = "66--70",
year = "1994",
keywords = "two-dimensional translation invariant wavelet
representation. sensitivity. two-dimensional signals.
fast algorithm. circular translates. input image.
optimal translate. decomposition. quadtree search
algorithm. complexity. translation invariant wavelet
transform. data compression.",
abstract = "Addresses the problem of the sensitivity of wavelet
representations to translations for two-dimensional
signals. The authors describe a fast algorithm to
calculate the two-dimensional wavelet transforms for
all the circular translates of an input image. They
select the optimal translate for the decomposition
using a quadtree search algorithm. The resulted wavelet
representation is invariant under translations measured
by an additive cost criterion. The complexity of the
whole algorithm is O(N/sup 2/ log N) for a N*N input
block. They apply this translation invariant wavelet
transform to data compression. The results show that by
taking into account the effect of translations,
additional compression can be achieved beyond that
achieved by a standard wavelet transform.",
}
@Article{lia-par:image,
title = "Image coding using translation invariant wavelet
transforms with symmetric extensions",
author = "Jie Liang and Thomas W. Parks",
journal = IEEETIP,
volume = "7",
number = "5",
year = "1998",
pages = "762--769",
keywords = "representation",
abstract = "In this correspondence, we address the problem of
translation sensitivity of conventional wavelet
transforms for two-dimensional (2-D) signals. We
propose wavelet transform algorithms that achieve the
following desirable properties simultaneously: i)
translation invariance, ii) reduced edge effects, and
iii) sice-limitedness. We apply this translation
invariant biorthogonal wavelet transform with symmetric
extensions to image coding applications with good
results.",
}
@Article{lia-par:translation,
title = "A translation-invariant wavelet representation
algorithm with applications",
author = "Jie Liang and Thomas W. Parks",
journal = IEEETSP,
volume = "44",
number = "2",
year = "1996",
pages = "225--232",
abstract = "We address the time-varying problem of wavelet
transforms, and a new translation-invariant wavelet
representation algorithm is proposed. Using the
algorithm introduced by Beylkin (see SIAM J. Numer.
Anal., vol. 29, p.1716-1740, 1992), we compute the
wavelet transform for all the circular time shifts of a
length- N signal in O(N log N) operations. The wavelet
coefficients of the time shift with minimal cost are
selected as the best representation of the signal using
a binary tree search algorithm with an appropriate cost
function. We apply the translation-invariant
representation algorithm to a geoacoustic data
compression application. The results show that the new
algorithm can reduce the distortion (the squared error
in our case) substantially, if the input signals are
transients that are sensitive to time shifts.",
}
@Article{lil-par:multiwavelet,
title = "Multiwavelet spectral and polarization analyses of
seismic records",
author = "J. M. Lilly and J. Park",
journal = GJI,
volume = "122",
number = "3",
year = "1995",
pages = "1001--1021",
keywords = "multiwavelet spectral analysis polarization analysis
seismic records wavelet transform multiple taper
spectral analysis low-variance spectrum estimate
nonstationary data process multiwavelet algorithm
mutually orthogonal Slepian wavelets time-varying
spectral density matrix three-component seismic data
three-component motion singular value decomposition
seismic body waves elliptical polarization polarization
estimators earthquakes",
abstract = "Presents an algorithm, based on the wavelet transform
and multiple taper spectral analysis, for providing a
low-variance spectrum estimate of a non-stationary data
process. The `multiwavelet' algorithm uses, within each
frequency band, a number of mutually orthogonal Slepian
wavelets, optimally concentrated in frequency. The sum
of squared wavelet transforms with the Slepian wavelets
results in a spectrum estimate that is both
low-variance and resistant to broad-band bias. The
multiwavelet algorithm is used to estimate the
time-varying spectral density matrix S(f,t) for two or
more time series, in particular for three-component
seismic data. Coherent three-component motion is
described by motion along a single trajectory, with
appropriate projections onto the three component axes.
This trajectory is found by applying a singular value
decomposition (SVD) to a matrix M(f,t) of wavelet
transform values. The normalized first singular value
of the SVD determines whether a correlation among the
three components of the seismogram is statistically
significant. Where significant, coherent particle
motion is reconstructed by a linear combination of the
wavelets with coefficients specified by the first
left-singular vector. The polarization of this motion
with respect to the coordinate axes is given by the
first right-singular vector. Where the wavelets are
real-valued, the usefulness of this method is limited
to cases in which the three components of the seismic
record oscillate in phase with each other, as is often
the case for seismic body waves. Elliptical
polarization is handled by pairing even and odd Slepian
wavelets into complex-valued wavelets, capable of
detecting phase shifts between components. The authors
demonstrate the multiwavelet spectrum and polarization
estimators on seismic data from a large shallow
earthquake in the Solomon Islands, and from the deep
earthquakes beneath Fiji (1994 March 9) and Bolivia
(1994 June 9).",
}
@Article{lin-per-rot:ice,
title = "The Discrete Wavelet Transform and the Scale Analysis
of the Surface Properties of Sea Ice",
author = "Ronald W. Lindsay and Donald B. Percival and D. Andrew
Rothrock",
journal = IEEETGRS,
volume = "34",
number = "3",
year = "1996",
pages = "771--787",
keywords = "Sea ice; Radar remote sensing; Discrete wavelet
transform; Scale analysis; Daubechies wavelet filter;
scale-dependent wavelet variance; Wavelet covariance;
Mallat orthogonal-pyramid algorithm; Spring pack ice;
Beaufort Sea",
abstract = "The formalism of the one-dimensional discrete wavelet
transform (DWT) based on Daubechies wavelet filters is
outlined in terms of finite vectors and matrices. Both
the scale-dependent wavelet variance and wavelet
covariance are considered and confidence intervals for
each are determined. The variance estimates are more
accurately determined with a maximal-overlap version of
the wavelet transform. The properties of several
Daubechies wavelet filters and the associated basis
vectors are discussed. Both the Mallat
orthogonal-pyramid algorithm for determining the DWT
and a pyramid algorithm for determining the
maximal-overlap version of the transform are presented
in terms of finite vectors. As an example, the authors
investigate the scales of variability of the surface
temperature and albedo of spring pack ice in the
Beaufort Sea. The data analyzed are from individual
lines of a Landsat TM image (25-m sample interval) and
include both reflective (channel 3, 30-m resolution)
and thermal (channel 6, 120-m resolution) data. The
wavelet variance and covariance estimates are presented
and more than half of the variance is accounted for by
scales of less than 800 m. A wavelet-based technique
for enhancing the lower-resolution thermal data using
the reflected data is introduced. The simulated effects
of poor instrument resolution on the estimated lead
number density and the mean lead width are investigated
using a wavelet-based smooth of the observations.",
}
@InCollection{liu:new-perspective,
title = "Wavelet Transform and New Perspective on Coastal and
Ocean Engineering Data Analysis",
booktitle = "Advances in Coastal and Ocean Engineering",
author = "P. C. Liu",
editor = "P. L-F Liu",
volume = "6",
pages = "???--???",
year = "2000",
email = "liu@glerl.noaa.gov",
abstract = "",
}
@InCollection{liu:wavelet-spectrum,
title = "Wavelet Spectrum Analysis and Ocean Wind Waves",
author = "Paul C. Liu",
pages = "151--166",
email = "liu@glerl.noaa.gov",
crossref = "fou-kum:geophysics",
abstract = "",
}
@InCollection{lum-etal:optimization,
title = "Optimization of Bias-Variance Trade-Off in Non
Parametric Spectral Analysis by Decomposition into
Wavelet Packets",
author = "B. Lumeau and J. C. Pesquet and J. F. Bercher and
L. Louveau",
pages = "285--290",
crossref = "mey-roq:progress",
}
@TechReport{ma-str-vid:first-moment,
title = "The First Moment of Wavelet Random Variables",
author = "Yanyuan Ma and Gilbert Strang and Brani Vidakovic",
number = "97-10",
institution = "Institute of Statistics and Decision Sciences, Duke
University",
year = "1997",
URL = "ftp://ftp.isds.duke.edu/pub/WorkingPapers/97-10.ps",
}
@Article{mah:eddy,
title = "Eddy asymmetry in the sheared heated boundary layer",
author = "L. Mahrt",
journal = JAS,
volume = "48",
number = "3",
year = "1991",
pages = "472--482",
abstract = "Statistical measures are developed to study the
influence of mean shear on the asymmetry of eddy
updrafts as observed from low-level aircraft flights in
HAPEX, FIFE, and SESAME. This asymmetry involves
formation of microfronts between updrafts with slow
horizontal motion and downdrafts with faster horizontal
motion. The variance of the Haar-wavelet transform
(step-function basis) is found to be a superior
indicator of the dominant scales of such eddies
compared to the structure function. For those analyses
where scale dependence is not of interest, the simpler
structure function is applied. The coherent structures
at the dominant scale are examined by computing
eigenvectors of the lagged correlation matrix based on
conditionally sampled events.",
}
@Article{mak:sst,
title = "Orthogonal wavelet analysis: {I}nterannual variability
in the sea surface temperature",
author = "Mankin Mak",
journal = BAMetS,
volume = "76",
year = "1995",
pages = "2179--2186",
keywords = "ocean, environmental aspects, signal processing
technique, ocean temperature analysis",
abstract = "The unique capability of orthogonal wavelets, which
have attractive time-frequency localization properties
as exemplified by the Meyer wavelet, is demonstrated in
a diagnosis of the interannual variability using a
44-year dataset of the sea surface temperature (SST).
This wavelet analysis is performed in conjunction with
an empirical orthogonal function analysis and a Fourier
analysis to illustrate their complementary capability.
The focus of this article is on the equatorial Pacific
SST, which is known to have far-reaching impacts on
short-term climate variability. The Meyer spectrum
brings to light intriguing episodic characteristics of
three separate sequences of El Ni{\~n}o (abnormally
warm) and La Ni{\~n}a (abnormally cold) events during
the past 42 years. It quantifies the relative
contributions to the variability associated with
different frequency ranges at different times. Through
a wavelet cross-spectral analysis with the SST at an
equatorial location and at a midlatitude location in
the Pacific Ocean, the planetary character of the SST
field associated with such events is also
illustrated.",
}
@Article{mal-hwa:singularity,
title = "Singularity detection and processing with wavelets",
author = "S. G. Mallat and W. L. Hwang",
journal = IEEETIT,
volume = "38",
number = "2",
year = "1992",
pages = "617--643",
URL = "ftp://cs.nyu.edu/pub/tech-reports/tr549-R245.ps.Z",
keywords = "one dimensional signals, signal analysis, signal
processing, image edge location, white noise removal,
image processing, singularities, Lipschitz exponents,
wavelet transform, irregular structures, fast
oscillations, modulus maxima, two-dimensional signals",
abstract = "The mathematical characterization of singularities
with Lipschitz exponents is reviewed. Theorems that
estimate local Lipschitz exponents of functions from
the evolution across scales of their wavelet transform
are reviewed. It is then proven that the local maxima
of the wavelet transform modulus detect the locations
of irregular structures and provide numerical
procedures to compute their Lipschitz exponents. The
wavelet transform of singularities with fast
oscillations has a particular behavior that is studied
separately. The local frequency of such oscillations is
measured from the wavelet transform modulus maxima. It
has been shown numerically that one- and
two-dimensional signals can be reconstructed, with a
good approximation, from the local maxima of their
wavelet transform modulus. As an application, an
algorithm is developed that removes white noises from
signals by analyzing the evolution of the wavelet
transform maxima across scales. In two dimensions, the
wavelet transform maxima indicate the location of edges
in images.",
}
@Article{mal-pap-zha:covariance,
title = "Adaptive covariance estimation of locally stationary
processes",
author = "S. Mallat and G. Papicolaou and Z. Zhang",
journal = AofS,
volume = "26",
number = "1",
year = "1998",
pages = "1--47",
URL = "ftp://math.Stanford.EDU/pub/papers/papanicolaou/lsb.ps.gz",
keywords = "",
abstract = "",
}
@Article{mal-zha:matching,
title = "Matching pursuits with time-frequency dictionaries",
author = "S. Mallat and Z. Zhang",
journal = IEEETSP,
volume = "41",
number = "12",
year = "1993",
pages = "3397--3415",
keywords = "",
abstract = "",
}
@Article{mal-zho:characterization,
title = "Characterization of signals from multiscale edges",
author = "S. Mallat and S. Zhong",
journal = IEEETPAMI,
volume = "14",
number = "7",
year = "1992",
pages = "710--732",
keywords = "1D signals, 2D signals, picture processing, multiscale
Canny edge detection, local maxima, wavelet theory,
pattern recognition, multiscale edge representation,
image coding",
abstract = "A multiscale Canny edge detection is equivalent to
finding the local maxima of a wavelet transform. The
authors study the properties of multiscale edges
through the wavelet theory. For pattern recognition,
one often needs to discriminate different types of
edges. They show that the evolution of wavelet local
maxima across scales characterize the local shape of
irregular structures. Numerical descriptors of edge
types are derived. The completeness of a multiscale
edge representation is also studied. The authors
describe an algorithm that reconstructs a close
approximation of 1-D and 2-D signals from their
multiscale edges. For images, the reconstruction errors
are below visual sensitivity. As an application, a
compact image coding algorithm that selects important
edges and compresses the image data by factors over 30
has been implemented.",
}
@Article{mal:multiresolution,
title = "A theory for multiresolution signal decomposition:
{T}he wavelet representation",
author = "S. Mallat",
journal = IEEETPAMI,
volume = "11",
number = "7",
year = "1989",
pages = "674--693",
keywords = "picture processing, encoding, pattern recognition,
multiresolution signal decomposition, wavelet
representation, pyramidal algorithm, convolutions,
quadrature mirror filters, data compression, image
coding, texture discrimination, fractal analysis",
abstract = "Multiresolution representations are effective for
analyzing the information content of images. The
properties of the operator which approximates a
signal at a given resolution were studied. It is
shown that the difference of information between the
approximation of a signal at the resolutions 2/sup
j+1/ and 2/sup j/ (where j is an integer) can be
extracted by decomposing this signal on a wavelet
orthonormal basis of L/sup 2/(R/sup n/), the vector
space of measurable, square-integrable n-dimensional
functions. In L/sup 2/(R), a wavelet orthonormal
basis is a family of functions which is built by
dilating and translating a unique function psi
(x). This decomposition defines an orthogonal
multiresolution representation called a wavelet
representation. It is computed with a pyramidal
algorithm based on convolutions with quadrature
mirror filters. Wavelet representation lies between
the spatial and Fourier domains. For images, the
wavelet representation differentiates several
spatial orientations. The application of this
representation to data compression in image coding,
texture discrimination and fractal analysis is
discussed.",
}
@Book{mal:tour,
title = "A Wavelet Tour of Signal Processing",
author = "St\'{e}phane Mallat",
publisher = "Academic Press",
address = "San Diego",
year = "1998",
keywords = "",
abstract = "A Wavelet Tour of Signal Processing begins with a
presentation of the wonders of the Fourier
transform, and then describes its failures for
transient signal processing. It presents local
time-frequency methods and the related mathematical
tools. The book uses an intuitive approach to
important mathematical results, and emphasizes
practical applications rather than proofs. It
describes numerical discrete algorithms as well as
some applications to information processing, fractal
analysis, noise removal, and compact signal
coding. A Wavelet Tour of Signal Processing is
intended for signal processing engineers who want to
discover the potential applications of recent
mathematical advances in time-frequency signal
representations. Of interest to researchers in
applied mathematics, the book highlights the
applications of these new techniques and also
provides an overview of signal processing problems",
}
@Article{mal:vision,
title = "{W}avelets for a vision",
author = "S. Mallat",
journal = PIEEE,
volume = "84",
number = "4",
year = "1996",
pages = "604--614",
abstract = "Early on, computer vision researchers have realized
that multiscale transforms are important to analyze the
information content of images. The wavelet theory gives
a stable mathematical foundation to understand the
properties of such multiscale algorithms. This tutorial
describes major applications to multiresolution search,
multiscale edge detection, and texture
discrimination.",
}
@Article{mal:zero,
title = "Zero-crossings of a wavelet transform",
author = "S. G. Mallat",
journal = IEEETIT,
volume = "37",
number = "4",
year = "1991",
pages = "1019--1033",
keywords = "signal reconstruction, wavelet transform,
completeness, stability, pattern recognition,
multiscale representation, zero-crossings, projection
algorithm, fast convergence, iteration, coarse-to-fine
stereo-matching algorithm",
abstract = "The completeness, stability, and application to
pattern recognition of a multiscale representation
based on zero-crossings is discussed. An alternative
projection algorithm is described that reconstructs a
signal from a zero-crossing representation, which is
stabilized by keeping the value of the wavelet
transform integral between each pair of consecutive
zero-crossings. The reconstruction algorithm has a fast
convergence and each iteration requires O(N log/sup 2/
(N)) computation for a signal of N samples. The
zero-crossings of a wavelet transform define a
representation which is particularly well adapted for
solving pattern recognition problems. As an example,
the implementation and results of a coarse-to-fine
stereo-matching algorithm are described.",
}
@Proceedings{man-hus:asymptotic,
title = "Asymptotic Statistics: Proceedings of the fifth Prague
Symposium",
booktitle = "Asymptotic Statistics: Proceedings of the fifth Prague
Symposium",
editor = "Petr Mandl and Marie Huskova",
publisher = "Physica-Verlag",
address = "Heidelberg",
series = "Contributions to Statistics",
year = "1994",
}
@Article{man-lee:robust,
title = "Robust Estimation of Background Noise and Signal
Detection in Climatic Time Series",
author = "Michael E. Mann and Jonathan M. Lees",
journal = "Climate Change",
volume = "33",
year = "1996",
pages = "409--445",
URL = "http://love.geology.yale.edu/mtm/",
abstract = "We present a new technique for isolating climate
signals in time series with a characteristic 'red'
noise background which arises from temporal
persistence. This background is estimated by a 'robust'
procedure that, unlike conventional techniques, is
largely unbiased by the presence of signals immersed in
the noise. Making use of multiple-taper spectral
analysis methods, the technique further provides for a
distinction between purely harmonic (periodic) signals,
and broader-band ('quasiperiodic') signals. The
effectiveness of our signal detection procedure is
demonstrated with synthetic examples that simulate a
variety of possible periodic and quasiperiodic signals
immersed in red noise. We apply our methodology to
historical climate and paleoclimate time series
examples. Analysis of a approximate to 3 million year
sediment core reveals significant periodic components
at known astronomical forcing periodicities and a
significant quasiperiodic 100 year peak. Analysis of a
roughly 1500 year tree-ring reconstruction of
Scandinavian summer temperatures suggests significant
quasiperiodic signals on a near-century timescale, an
interdecadal 16-18 year timescale, within the
interannual El Ninio/Southem Oscillation (ENSO) band,
and on a quasibiennial timescale. Analysis of the 144
year record of Great Salt Lake monthly volume change
reveals a significant broad band of significant
interdecadal variability, ENSO-timescale peaks, an
annual cycle and its harmonics. Focusing in detail on
the historical estimated global-average surface
temperature record, we find a highly significant
secular trend relative to the estimated red noise
background, and weakly significant quasiperiodic
signals within the ENSO band. Decadal and quasibiennial
signals are marginally significant in this series.",
}
@Article{man-wal:stochastic,
title = "On stochastic limit and order relationships",
author = "H. B. Mann and A. Wald",
journal = AofMS,
volume = "14",
year = "1943",
pages = "217--226",
}
@Article{man:multifractal,
title = "A Multifractal Walk Down Wall Street",
author = "Benoit B. Mandelbrot",
journal = "Scientific American",
month = "February",
year = "1999",
pages = "50--53",
}
@Unpublished{mar-ada-joh-neu-pat:exact,
title = "Exact Risk Analysis of Wavelet Regression",
author = "S. J. Marron and S. Adak and Iain Johnstone and
Michael H. Neumann and P. Patil",
year = "1996",
note = "To appear in {\em Journal of Computational and
Graphical Statistics}",
}
@Article{mar-wil:indirect,
title = "Indirect estimation of {ARFIMA} and {VARFIMA}
models",
author = "Martin, V. L. and Wilkins, N. P.",
journal = JEcon,
volume = "93",
number = "1",
year = "1999",
pages = "149--175",
abstract = "Indirect estimation methods are proposed for
estimating ARFIMA, as well as more complex VARFIMA
models. A general framework for conducting indirect
estimation of fractional models is developed that
covers simulation methods, choice of auxiliary model
and estimation algorithm. Special attention is given
to comparing the finite sampling properties of the
indirect estimator with Sowell's (1992a) exact time
domain maximum-likelihood estimator, the spectral
maximum-likelihood estimator of Fox and Taqqu (1986)
and the Geweke and Porter-Hudak (1983) spectral
regression estimator. The indirect estimator can be
computationally faster than the exact time domain
maximum-likelihood estimator while generating
similar small sample properties. The computational
gains of the indirect estimator over maximum
likelihood increase as the complexity of the data
generating process increases."
}
@Article{mar:effective,
title = "Effective writing in mathematical statistics",
author = "J. S. Marron",
journal = SN,
volume = "53",
number = "1",
year = "1999",
pages = "68--75",
}
@Article{mas:application,
title = "The wavelet transform of stochastic processes with
stationary increments and its application to fractional
{B}rownian motion",
author = "Elias Masry",
journal = IEEETIT,
volume = "39",
number = "1",
year = "1993",
pages = "260--264",
keywords = "wavelet transform, stochastic processes, fractional
Brownian motion, random processes, wide-sense
stationary increments, correlation function, spectral
distribution, orthonormal series expansion, spectral
analysis",
abstract = "The wavelet transform of random processes with
wide-sense stationary increments is shown to be a
wide-sense stationary process whose correlation
function and spectral distribution are determined. The
second-order properties of the coefficients in the
wavelet orthonormal series expansion of such processes
is obtained. Applications to the spectral analysis and
to the synthesis of fractional Brownian motion are
given.",
}
@Article{mas:convergence,
title = "Convergence properties of wavelet series expansions of
fractional {B}rownian motion",
author = "Elias Masry",
journal = ACHA,
volume = "3",
number = "3",
year = "1996",
pages = "239--253",
keywords = "convergence properties, wavelet series expansions,
Brownian motion, approximation error, finite intervals,
convergence rates, signal processing",
abstract = "We consider the approximation of a fractional Brownian
motion by a wavelet series expansion at resolution
$2^{-l}$. The approximation error is measured in the
integrated mean squared sense over finite intervals and
we obtain its expansion as a sum of terms with
increasing rates of convergence. The dependence of the
coefficients in the expansion of the error on the scale
function is explicitly determined.",
}
@TechReport{mcc-per-wal:phase,
title = "On the Phase of Least-Asymmetric Scaling and Wavelet
Filters",
author = "Emma J. McCoy and Donald B. Percival and Andrew T.
Walden",
institution = "Dept. of Mathematics, Imperial College of Science,
Technology and Medicine",
number = "TR-95-15",
year = "1995",
note = "Submitted to {\em IEEE Transactions on Signal
Processing}",
URL = "ftp://ftp.statsci.com/pub/WAVELETS/papers/wavephase.ps.gz",
abstract = "The advance applied to Daubechies' least-asymmetric
wavelet filters at each scale, in order to obtain near
zero phase, is derived. The appropriate advance depends
on whether half the length of each of the original
quadrature mirror filters is even or odd. The
departures from zero phase are illustrated.",
}
@Article{mcc-wal:long-memory,
title = "Wavelet Analysis and Synthesis of Stationary
Long-Memory Processes",
author = "Emma J. McCoy and Andrew T. Walden",
journal = JCGS,
volume = "5",
number = "1",
year = "1996",
pages = "26--56",
abstract = "The discrete wavelet transform (DWT) can be
interpreted as a filtering of a time series by a set of
octave band filters such that the width of each band as
a proportion of its center frequency is constant. A
long-memory process having a power spectrum that plots
as a straight line on log-frequency/log-power scales
over many octaves of frequency is intrinsically related
to such a structure. As an example of such processes,
we focus on one class of discrete-time, stationary,
long-memory processes, the fractionally differenced
Gaussian white noise processes (fdGn). We show how the
DWT breaks down a fdGn, and show the exact correlation
structure of the resulting coefficients for different
wavelets (Daubechies' minimum-phase and
least-asymmetric and Haar). The DWT is an impressive
``whitening filter.'' A discrete wavelet-based scheme
for simulating fdGn's is discussed and is shown to be
equivalent to a spectral decomposition of the
covariance matrix of the process; however, it can be
carried out using only information on the nature of the
spectrum of the process --- that is, time-domain
information is not required. It produces results
comparable with theexact Hosking method. We then show
that, using wavelet methods, the spectral slope
parameter $d$ can be estimated as well, or better, than
when using the best Fourier-based method known to us,
namely regression on multitaper spectral ordinates.
Since wavelet analysis and synthesis methods can be
applied to a much wider variety of empirical or
theoretical long-memory processes, wavelet methods
could prove a valuable tool in the future in the
analysis and synthesis of stochastic processes.",
}
@PhdThesis{mcc:thesis,
title = "Some New Statistical Approaches to the Analysis of
Long Memory Processes",
author = "Emma J. McCoy",
school = "Imperial College, UK, Deptartment of Mathematics",
year = "1994",
postscript = "http://www.ma.ic.ac.uk/statistics/links/stafflinks/ejm.link/papers/report.ps.gz",
}
@TechReport{mcn-mau:applications,
title = "Applications of wavelet analysis for determining
glucose concentration of aqueous solutions using
{NIR} spectroscopy",
author = "Christopher S. McNulty and Ganapati Mauze",
number = "HPL-98-53",
institution = "Hewlett-Packard Laboratories",
year = "1998",
URL = "http://www.hpl.hp.com/techreports/98/HPL-98-53.ps",
}
@Article{mee-esc:algorithm,
title = "An algorithm to compute the {CDF} of the product of
two normal random variables",
author = "William Q. Meeker and Luis A. Escobar",
journal = CSA,
volume = "23",
number = "1",
year = "1994",
pages = "271--280",
}
@Article{men:analysis,
title = "Analysis of turbulence in the orthonormal wavelet
representation",
author = "C. Meneveau",
journal = JFM,
volume = "232",
year = "1991",
pages = "469--520",
keywords = "turbulence, orthonormal wavelet, turbulent velocity
fields, wavelet-transformed Navier-Stokes equations,
kinetic energy, one-dimensional velocity signals,
boundary layer, turbulent wake, circular cylinder,
three-dimensional velocity fields, multifractal
scaling",
abstract = "A decomposition of turbulent velocity fields into
modes that exhibit both localization in wavenumber and
physical space is performed. The author reviews some
basic properties of such a decomposition, the wavelet
transform. The wavelet-transformed Navier-Stokes
equations are derived, and he defines new quantities
such as e(r,x), t(r,x) and pi (r,x) which are the
kinetic energy, the transfer of kinetic energy and the
flux of kinetic energy through scale r at position x.
The discrete version of e(r,x) is computed from
laboratory one-dimensional velocity signals in a
boundary layer and in a turbulent wake behind a
circular cylinder. The author also computes (r,x),
t(r,x) and pi (r,x) from three-dimensional velocity
fields obtained from direct numerical simulations. His
findings are that the localized kinetic energies become
very intermittent in x at small scales and exhibit
multifractal scaling. The transfer and flux of kinetic
energy are found to fluctuate greatly in physical space
for scales between the energy containing scale and the
dissipative scale.",
}
@InProceedings{men:mixed,
title = "Wavelet analysis of turbulence: {T}he mixed energy
cascade",
author = "C. Meneveau",
pages = "251--264",
crossref = "far-hun-vas:wavelets",
keywords = "wavelets, turbulence",
abstract = "The wavelet-transformed Navier-Stokes equations are
used to define quantities such as the transfer of
kinetic energy and the flux of kinetic energy by scale
and position. Direct numerical simulations are
performed which show large spatial variability at every
scale and non-Gaussian statistics. The local energy
flux exhibits large spatial intermittency and is often
negative, indicating local inverse cascades.",
}
@Article{mey-sel-taq:wavelets,
title = "Wavelets, generalized white noise and fractional
integration: {T}he synthesis of fractional
{B}rownian motion",
author = "Meyer, Y. and Sellan, F. and Taqqu, M. S.",
journal = JFAA,
volume = "5",
number = "5",
year = "1999",
pages = "465--494",
abstract = "We provide an almost sure convergent expansion of
fractional Brownian motion in wavelets which
decorrelates the high frequencies. Our approach
generalizes Levy's midpoint displacement technique
which is used to generate Brownian motion. The
low-frequency terms in the expansion involve all
independent fractional Brownian motion evaluated at
discrete times or, alternatively, partial sums of a
stationary fractional ARIMA time series. The
wavelets fill in the gaps and provide the necessary
high frequency corrections We also obtain a way of
constructing an arbitrary number of non-Gaussian
continuous time processes whose second order
properties are the same as those of fractional
Brownian motion.",
}
@Book{mey-roq:progress,
title = "Progress in Wavelet Analysis and Applications",
booktitle = "Progress in Wavelet Analysis and Applications",
editor = "Yves Meyer and Sylvie Roques",
publisher = "Editions Fronti{\`e}res",
address = "Paris",
year = "1993",
pages = "785",
}
@Book{mey:algorithms,
title = "Wavelets: Algorithms \& Applications",
author = "Yves Meyer",
publisher = SIAM,
address = "Philadelphia",
year = "1993",
keywords = "Wavelets, Mathematics",
note = "Translated and revised by Robert D. Ryan",
loc = "QA403.3 .M4913 1993",
}
@Book{mey:wavelets,
title = "Wavelets and Operators",
author = "Yves Meyer",
publisher = "Cambridge University Press",
series = "Cambridge Studies in Advanced Mathematics 37",
year = "1992",
note = "Translated to English by D. H. Salinger",
ISBN = "0-521-42000-8",
keywords = "Fourier Series and Integrals, Filtering and Sampling /
Multiresolution Approximation of L2(Rn) / Orthonormal
Wavelet Bases / Non-orthogonal Wavelets / Wavelets the
Hardy Space H1 and Its Dual BMO / Wavelets and Spaces
of Functions and Distributions",
URL = "http://www.cup.org/Titles/42/0521420008.html",
abstract = "The first book in English to provide a comprehensive
account of the mathematical theory of wavelets which
has proved to be a powerful tool for harmonic analysts,
and an alternative to the standard theory of Fourier
analysis",
}
@Article{mih-etal:low-complexity,
title = "Low-complexity image denoising based on statistical
modeling of wavelet coefficients",
author = "Mihcak, M. K. and Kozintsev, I. and Ramchandran,
K. and Moulin, P.",
journal = IEEESPL,
volume = "6",
number = "12",
year = "1999",
pages = "300--303",
abstract = "We introduce a simple spatially adaptive statistical
model for wavelet image coefficients and apply it to
image denoising, Our model is inspired by a recent
wavelet image compression algorithm, the
estimation-quantization (EQ) coder. We model wavelet
image coefficients as zero-mean Gaussian random
variables with high local correlation. We assume a
marginal prior distribution on wavelet coefficients
variances and estimate them using an approximate
maximum a posteriori probability rule. Then we apply
an approximate minimum mean squared error estimation
procedure to restore the noisy wavelet image
coefficients. Despite the simplicity of our method,
both in its concept and implementation, our
denoising results are among the best reported in the
literature."
}
@Article{mor-per:mbdtw,
title = "Minimum-bandwidth discrete-time wavelets",
author = "Morris, J. M. and Peravali, R.",
journal = SP,
volume = "76",
number = "2",
year = "1999",
pages = "181--193",
keywords = "minimum bandwidth wavelet transform discrete-time
wavelets adaptive simulated annealing",
abstract = "In this paper we present a class of
minimum-bandwidth, discrete-time orthonormal
wavelets (MBDTWs), The wavelets were generated via
the filter bank framework and were optimized using
the global optimization technique, adaptive
simulated annealing (ASA). The objective function is
the average normalized bandwidth of the wavelets
over all scales as obtained from the filter bank
structure. We tabulate the wavelet-defining low-pass
filter coefficients {g(n)} for filter lengths of N =
4, 8, 10, 12, 14, 16, 18, 24 and 32 and for L = 2, 3
and 4. We provide comparisons with Daubeohies'
discrete wavelets and other classes of optimum
wavelets. Finally, we present examples that
demonstrate the advantage of our MBDTWs for certain
narrowband applications: de-noising of an ECG
signal, and compression of an ECG signal and a bird
call signal. We compare the performance of our
wavelets in these examples with that of Daubechies'
least-asymmetric wavelets which are closest to the
MBDTWs with respect to our bandwidth measure.",
}
@InProceedings{mor:from,
title = "From Fourier to Wavelet Analysis of Time Series",
author = "Pedro A. Morettin",
booktitle = "Proceedings in Computational Statistics",
editor = "A. Prat",
year = "1996",
pages = "111--122",
}
@Article{mou:power,
title = "Wavelet Thresholding Techniques for Power Spectrum
Estimation",
author = "Pierre Moulin",
journal = IEEETSP,
volume = "42",
number = "11",
year = "1994",
pages = "3126--3136",
URL = "ftp://flash.bellcore.com/pub/moulin/wavSE.tar.Z",
abstract = "Estimation of the power spectrum S(f) of a stationary
random process can be viewed as a nonparametric
statistical estimation problem. We introduce a
nonparametric approach based on a wavelet
representation for the logarithm of the unknown S(f).
This approach offers the ability to capture
statistically significant components of ln S(f) at
different resolution levels and guarantees
nonnegativity of the spectrum estimator. The spectrum
estimation problem is set up as a problem of inference
on the wavelet coefficients of a signal corrupted by
additive non-Gaussian noise. We propose a wavelet
thresholding technique to solve this problem under
specified noise/resolution tradeoffs and show that the
wavelet coefficients of the additive noise may be
treated as independent random variables. The thresholds
are computed using a saddle-point approximation to the
distribution of the noise coefficients.",
}
@TechReport{mul-vid:density-estimation,
title = "Bayesian Inference with Wavelets: {D}ensity
Estimation",
author = "Peter M{\"u}ller and Brani Vidakovic",
year = "1995",
number = "95-34",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
URL = "http://www.isds.duke.edu/~brani/papers/ModMixWav.ps",
}
@TechReport{mul-vid:MCMC,
title = "{MCMC} Methods in Wavelet Shrinkage: {N}on-Equally
Spaced Regression, Density and Spectral Density
Estimation",
author = "Peter M{\"u}ller and Brani Vidakovic",
year = "1999",
number = "99-01",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
URL = "ftp://ftp.isds.duke.edu/pub/WorkingPapers/99-01.ps",
}
@Unpublished{mur-aus:using,
title = "Using the Wavelet Transform for Multivariate Data
Analysis and Time Series Forecasting",
author = "Fionn Murtagh and Alex Aussem",
year = "1996",
note = "Proc. IFCS'96, Kobe, Springer-Verlag, accepted
(subject to minor revision)",
URL = "ftp://ftp.infm.ulst.ac.uk/pub/Papers/neural-nets/kobe.ps",
}
@Unpublished{mur:wedding,
title = "Wedding the Wavelet Transform and Multivariate Data
Analysis",
author = "Fionn Murtagh",
year = "1996",
note = "To appear {\em Journal of Classification}",
URL = "ftp://ftp.infm.ulst.ac.uk/pub/Papers/neural-nets/wt-mda-new.ps",
}
@Book{mye:book,
title = "Classical and Modern Regression with Applications",
author = "Raymond H. Myers",
edition = "2",
publisher = "PWS--KENT",
address = "Boston",
series = "The Duxbury Advanced Series in Statistics and Decision
Sciences",
year = "1990",
}
@TechReport{nas-sap-saw:modelling,
title = "Statistical modelling of time series using
non-decimated wavelet representations",
author = "G. P. Nason and T. Sapatinas and A. Sawczenko",
institution = "Department of Mathematics, University of Bristol,
Bristol",
year = "1997",
URL = "http://www.stats.bris.ac.uk/pub/reports/Wavelets/smotsunwr.ps.gz",
}
@InProceedings{nas-sil:stationary,
title = "The Stationary Wavelet Transform and some Statistical
Applications",
author = "Guy P. Nason and Bernard W. Silverman",
pages = "281--300",
URL = "http://www.stats.bris.ac.uk:81/pub/reports/Silverman/swtsa.ps.gz",
crossref = "ant-opp:wavelets",
abstract = "",
}
@Article{nas-sil:transform,
title = "The Discrete Wavelet Transform in {S}",
author = "Guy P. Nason and Bernard W. Silverman",
journal = JCGS,
volume = "3",
number = "2",
pages = "163--191",
year = "1994",
URL = "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/tdwtis.ps.gz",
keywords = "Curve estimation; Image compression; Nonparametric
regression; Smoothing; Software; Statistical
algorithms; Thresholding",
abstract = "The theory of wavelets has recently undergone a period
of rapid development. We introduce a software package
called {\tt wavethresh} that works within the
statistical language S to perform one- and
two-dimensional discrete wavelet transforms. The
transforms and their inverses can be computed using any
particular wavelet selected from a range of different
families of wavelets. Pictures can be drawn of any of
the one- or two-dimensional wavelets available in the
package. The wavelet coefficients can be presented in a
variety of ways to aid in the interpretation of data.
The package's wavelet transform ``engine'' is written
in C for speed and the object-oriented functionality of
S makes {\tt wavethresh} easy to use. We provide a
tutorial introduction to wavelets and the {\tt
wavethresh} software. We also discuss how the software
may be used to carry out nonlinear regression and image
compression. In particular, thresholding of wavelet
coefficients is a method for attempting to extract
signal from noise and {\tt wavethresh} includes
functions to perform thresholding according to methods
in the literature.",
}
@InCollection{nas-sil:wavelets,
title = "Wavelets for regression and other statistical
problems",
author = "Guy P. Nason and Bernard W. Silverman",
booktitle = "Smoothing and Regression: Approaches, Computation and
Application",
editor = "M. G. Schimek",
publisher = "Wiley",
year = "1997",
}
@Article{nas-von:witsa,
title = "Wavelets in time series analysis",
author = "Guy P. Nason and Rainer {von Sachs}",
journal = PTRSLA,
volume = "357",
number = "1760",
year = "1999",
pages = "2511--2526",
}
@Unpublished{nas-von-kro:evolutionary,
title = "Wavelet processes and adaptive estimation of the
evolutionary wavelet spectrum",
author = "Guy P. Nason and Rainer {von Sachs} and Gerald
Kroisandt",
year = "2000",
URL = "http://playfair.Stanford.EDU/reports/rvs/NvSK.ps.Z",
note = "{\em Journal of the Royal Statistical Society Series
B}, to appear",
}
@InProceedings{nas:choice,
title = "Choice of the threshold parameter in wavelet function
estimation",
author = "Guy P. Nason",
pages = "261--280",
crossref = "ant-opp:wavelets",
URL = "",
note = "",
abstract = "",
}
@TechReport{nas:regression,
title = "Wavelet regression by cross-validation",
author = "Guy P. Nason",
year = "1994",
institution = "Deptartment of Mathematics, University of Bristol",
URL = "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/wvcx.ps.gz",
pages = "45",
keywords = "wavelets",
abstract = "This paper is about using wavelets for regression. The
main aim is to introduce and develop a cross-validation
method for selecting a wavelet regression threshold
that produces good estimates with respect to $L_2$
error. The selected threshold determines which
coefficients to keep in an orthogonal wavelet expansion
of noisy data and acts in a similar way to a smoothing
parameter in non-parametric regression.",
}
@Article{nas:shrinkage,
title = "Wavelet shrinkage by cross-validation",
author = "Guy P. Nason",
journal = JRSSB,
volume = "58",
year = "1996",
pages = "463--479",
URL = "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/wvcxPAPER.ps.gz",
abstract = "Wavelets are orthonormal basis functions with special
properties that show potential in many areas of
mathematics and statistics. This paper concentrates on
the estimation of functions and images from noisy data
by using wavelet shrinkage. A modified form of twofold
cross-validation is introduced to choose a threshold
for wavelet shrinkage estimators operating on data sets
of length a power of 2. The cross-validation algorithm
is then extended to data sets of any length and to
multidimensional data sets.The algorithms are compared
with established threshold choosers by using
simulation. An application to a real data set arising
from anaesthesia is presented.",
keywords = "ADAPTIVE ESTIMATION ANAESTHETICS NONPARAMETRIC
REGRESSION SMOOTHING PARAMETER SPATIAL ADAPTATION
THRESHOLD",
}
@Article{nas:wavelets,
title = "Wavelets",
author = "Guy P. Nason",
journal = "New Electronics",
month = apr,
year = "1997",
URL = "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/ne.ps.gz",
}
@Unpublished{nav-bro:dependence,
title = "Dependence Structure of Random Wavelets Coefficients
in function of higher Cumulants for Non-Gaussian and
Non-Linear processes",
author = "Philippe Naveau and Peter Brockwell",
year = "1999",
note = "Geophysical Statistics Project, National Center for
Atmospheric Research",
}
@Unpublished{nav-etal:exploratory,
title = "Exploratory statistical analysis of tropical oceanic
convection using discrete wavelet transforms",
author = "Philippe Naveau and Mitchell Moncrieff and Jun-Ichi
Yano and Xiaoqing Wu",
year = "1999",
note = "Submitted in the book ``Case Studies in Statistics
and the Atmospheric Sciences''",
}
@Article{nen-rid-zei:infrared,
title = "Wavelet analysis of low altitude infrared
transmission in the coastal environment",
author = "Nener, B. D. and Ridsdill-Smith, T. A. and Zeisse,
C.",
journal = "Infrared Physics and Technology",
volume = "40",
number = "5",
year = "1999",
pages = "399--409",
abstract = "Analysis of medium and long wavelength infrared
light transmission measurements collected during an
intensive experimental investigation over San Diego
Bay, CA, USA, has been performed using Morlet
wavelets. Wavelet analysis shows locally periodic
trends in signals and shows how these trends evolve
in time. The analysis has shown the effect of the
relative humidity and the windspeed on the
transmission in both mid- and long-wave bands of the
LR. The effect of air mass parameter does not appear
to be strongly correlated. The wavelet
representations of the data given in the figures
provide a useful overview of the effects of the
atmosphere on infrared transmission.",
}
@Article{neu-von:anisotropic,
title = "Wavelet thresholding in anisotropic function classes
and application to adaptive estimation of evolutionary
spectra",
author = "Michael H. Neumann and Ranier von Sachs",
journal = AofS,
volume = "25",
number = "1",
year = "1997",
pages = "38--76",
abstract = "",
}
@InCollection{neu-von:beyond,
title = "Wavelet thresholding: {B}eyond the {G}aussian {I.I.D}
situation",
author = "Michael H. Neumann and Ranier von Sachs",
pages = "301--329",
crossref = "ant-opp:wavelets",
abstract = "",
}
@TechReport{neu:spectral94,
title = "Spectral Density Estimation via Nonlinear Wavelet
Methods for Stationary Non-Gaussian Time Series",
author = "Michael H. Neumann",
year = "1994",
institution = "Statistics Research Report SRR 028-94, CMA, Australian
National University, Canberra",
URL = "http://wilton.anu.edu.au/research.reports/94srr.html",
}
@Article{neu:spectral96,
title = "Spectral Density Estimation via Nonlinear Wavelet
Methods for Stationary Non-Gaussian Time Series",
author = "Michael H. Neumann",
journal = JTSA,
volume = "17",
number = "6",
year = "1996",
pages = "601--633",
abstract = "In the present paper we consider nonlinear wavelet
estimators of the spectral density f of a zero mean,
not necessarily Gaussian, stochastic process, which is
stationary in the wide sense. It is known in the case
of Gaussian regression that these estimators outperform
traditional linear methods if the degree of smoothness
of the regression function varies considerably over the
interval of interest. Such methods are based on a
nonlinear treatment of empirical coefficients that
arise from an orthonormal series expansion according to
a wavelet basis. The main goal of this paper is to
transfer these methods to spectral density estimation.
This is done by showing the asymptotic normality of
certain empirical coefficients based on the tapered
periodogram.Using these results we can show the risk
equivalence to the Gaussian case for monotone
estimators based on such empirical coefficients. The
resulting estimator of f keeps all interesting
properties such as high spatial adaptivity that are
already known for wavelet estimators in the case of
Gaussian regression. It turns out that appropriately
tuned versions of this estimator attain the optimal
uniform rate of convergence of their L 2 risk in a wide
variety of Besov smoothness classes, including classes
where linear estimators (kernel, spline) are not able
to attain this rate. Some simulations indicate the
usefulness of the new method in cases of high spatial
inhomogeneity.",
keywords = "Spectral density estimation wavelet estimators
nonlinear wavelet shrinkage asymptotic normality large
deviations",
}
@Article{new:analysis1,
title = "{W}avelet analysis of vibration, {P}art {I}: theory",
journal = "Transactions of the ASME. Journal of Vibration and
Acoustics",
volume = "116",
number = "4",
year = "1994",
pages = "409--416",
author = "D. E. Newland",
abstract = "Wavelets provide a new tool for the analysis of
vibration records. They allow the changing spectral
composition of a nonstationary signal to be measured
and presented in the form of a time-frequency map. The
purpose of this paper, which is Part I of a pair, is to
introduce and review the theory of orthogonal wavelets
and their application to signal analysis. It includes
the theory of dilation wavelets, which have been
developed over a period of about ten years, and of
harmonic wavelets which have been proposed recently by
the author. Part II is about presenting the results on
wavelet maps and gives a selection of examples. The
papers will interest those who work in the field of
vibration measurement and analysis and who are in
positions where it is necessary to understand and
interpret vibration data.",
keywords = "wavelet analysis. vibration. changing spectral
composition. nonstationary signal. time-frequency map.
orthogonal wavelets. signal analysis. dilation
wavelets. harmonic wavelets. wavelet maps. vibration
measurement.",
}
@Article{new:analysis2,
title = "{W}avelet analysis of vibration, {P}art 2: wavelet
maps",
journal = "Transactions of the ASME. Journal of Vibration and
Acoustics",
volume = "116",
number = "4",
year = "1994",
pages = "417--25",
author = "D. E. Newland",
abstract = "For pt. 1, see ibid., vol. 116, p. 409-16, (1994).
Wavelet maps provide a graphical picture of the
frequency composition of a vibration signal. This
paper, which is Part 2 of a pair, describes their
construction and properties. In the case of harmonic
wavelets, there are close similarities between wavelet
maps and sonograms. A range of practical examples
illustrate how the wavelet method may be applied to
vibration analysis and some of its advantages.",
keywords = "wavelet maps. graphical picture. frequency
composition. vibration signal. harmonic wavelets.
sonograms. vibration analysis.",
}
@Book{new:book3,
title = "An Introduction to Random Vibrations, Spectral \&
Wavelet Analysis",
author = "David Edward Newland",
edition = "3",
publisher = "Longman Scientific \& Technical",
address = NY,
year = "1993",
pages = "477",
ISBN = "0-470-22153-4",
keywords = "Random vibration, Spectral theory, Mathematics, Data
processing, Wavelets",
}
@Article{new:harmonic,
title = "{H}armonic wavelet analysis",
journal = PRSLA,
volume = "443",
number = "1917",
year = "1993",
pages = "203--225",
author = "D. E. Newland",
keywords = "harmonic wavelet. frequency spectrum. octave band.
fast Fourier transform. Fourier coefficients. FFT.
inverse transform.",
abstract = "A new harmonic wavelet is suggested. Unlike wavelets
generated by discrete dilation equations, whose shape
cannot be expressed in functional form, harmonic
wavelets have the simple structure w(x)=(exp(i4 pi
x)-exp(i2 pi x))/i2 pi x. This function w(x) is
concentrated locally around x=0, and is orthogonal to
its own unit translations and octave dilations. Its
frequency spectrum is confined exactly to an octave
band so that it is compact in the frequency domain
(rather than in the x domain). An efficient
implementation of a discrete transform using this
wavelet is based on the fast Fourier transform (FFT).
Fourier coefficients are processed in octave bands to
generate wavelet coefficients by an orthogonal
transformation which is implemented by the FFT. The
same process works backwards for the inverse
transform.",
}
@Article{new:properties,
title = "Some properties of discrete wavelet maps",
author = "D. E. Newland",
journal = PEM,
volume = "9",
number = "1",
year = "1994",
pages = "59--69",
}
@Article{nin:estimation,
title = "Estimation of 1/f noise",
author = "B. Ninness",
journal = IEEETIT,
volume = "44",
number = "1",
pages = "32--46",
year = "1998",
keywords = "flicker noise fractional Brownian motion Hurst
exponent maximum-likelihood estimation 1/f noise
wavelet analysis",
abstract = "Several models have emerged for describing 1/f(gamma)
noise processes. Based on these, various techniques for
estimating the properties of such processes have been
developed. This paper provides theoretical analysis of
a new wavelet-based approach which has the advantages
of having low computational complexity and being able
to handle the case where the 1/f(gamma) noise might be
embedded in a further white-noise process. However, the
analysis conducted here shows that these advantages are
balanced by the fact that the wavelet-based scheme is
only consistent for spectral exponents gamma in the
range gamma is an element of (0, 1). This is in
contradiction to the results suggested in previous
empirical studies. When gamma is an element of (0, 1)
this paper also establishes that wavelet-based
maximum-likelihood methods are asymptotically Gaussian
and efficient. Finally, the asymptotic rate of
mean-square convergence of the parameter estimates Is
established and is shown to slow as gamma approaches
one. Combined with a survey of non-wavelet-based
methods, these new results give a perspective on the
various tradeoffs to be considered when modeling and
estimating 1/f(gamma) noise processes",
}
@Unpublished{now:shift-invariant,
title = "Shift invariant wavelet-based statistical models and
$1/f$ processes",
author = "R. D. Nowak",
note = "IEEE DSP Workshop, Bryce Canyon, UT",
year = "1998",
}
@Unpublished{ode-bur:class,
title = "New Class of Wavelets for Signal Approximation",
author = "Jan E. Odegard and C. Signey Burrus",
note = "Department of Electrical and Computer Engineering,
Rice University",
year = "1996",
email = "odegard@rice.edu, csb@rice.edu",
}
@InProceedings{ogd-che:abrupt,
title = "Testing for Abrupt Jumps with Wavelets",
author = "R. Todd Ogden and Cheng Cheng",
booktitle = "Proceedings of the 1997 Conference on the Interface of
Statistics and Computer Science",
pages = "",
year = "1997",
}
@Article{ogd-hil:2D,
title = "Data Analytic Wavelet Threshold Selection in 2-{D}
Signal Denoising",
author = "R. Todd Ogden and M. Hilton",
journal = IEEETSP,
volume = "45",
number = "2",
year = "1997",
pages = "496--500",
URL = "http://www.stat.sc.edu/~ogden/papers/technote.ps",
abstract = "A data adaptive scheme for wavelet shrinkage-based
noise removal is developed. The method involves a
statistical test of hypothesis that takes into account
the wavelet coefficients' magnitudes and relative
positions. The amount of smoothing performed during
noise removal is controlled by the user-supplied
confidence level of the tests.",
}
@InBook{ogd-lyn:bayesian,
title = "Bayesian analysis of change-point models",
authors = "R. Todd Ogden and James D. Lynch",
crossref = "mul-vid:biwbm",
pages = "???--???",
URL = "http://www.stat.sc.edu/~ogden/papers/springer4.ps",
}
@Article{ogd-par:change-point,
title = "Change-point Approach to Data Analytic Wavelet
Thresholding",
author = "R. Todd Ogden and Emanuel Parzen",
journal = SC,
volume = "6",
number = "2",
year = "1996",
pages = "93--99",
URL = "http://www.stat.sc.edu/~ogden/papers/datana.ps",
}
@Article{ogd-par:data-dependent,
title = "Data Dependent Wavelet Thresholding in Nonparametric
Regression with Change-point Applications",
author = "R. Todd Ogden and Emanuel Parzen",
journal = CSDA,
volume = "22",
year = "1996",
pages = "53--70",
URL = "http://www.stat.sc.edu/~ogden/papers/datdep.ps",
}
@Unpublished{ogd:bayesian,
title = "Wavelets in {B}ayesian Change-Point Analysis",
author = "R. Todd Ogden",
note = "Department of Statistics, University of South
Carolina",
year = "1996",
URL = "http://www.stat.sc.edu/~ogden/papers/bayes.ps",
}
@Book{ogd:book,
title = "Essential Wavelets for Statistical Applications and
Data Analysis",
author = "R. Todd Ogden",
year = "1996",
publisher = "Birkhauser",
address = "Boston",
URL = "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3864-4",
abstract = "Exciting new developments in wavelet theory have
attracted much attention and sparked new research in
many fields of applied mathematics. New tools are
available for efficient data compression, image
analysis, and signal processing, and there is a great
deal of activity in developing new wavelet methods. The
same features that make wavelets useful in these fields
also make wavelets a natural and attractive choice in
many areas of statistical data analysis. {\em Essential
Wavelets for Statistical Applications and Data
Analysis} presents an accesible, introductory survey
for new wavelet analysis tools and how they can be
applied to fundamental data analysis problems. A
variety of problems in statistics are discussed in a
non-theoretical style, with an emphasis on
understanding of wavelet methods. The only technical
prerequisite is basic knowledge of undergraduate
calculus, linear algebra, and basic statistical
theory.",
}
@Article{ogd:preconditioning,
title = "On Preconditioning the Data for the Wavelet
Transform When the Sample Size is Not a Power of
Two",
author = "R. Todd Ogden",
journal = CSB,
volume = "26",
year = "1997",
pages = "267--285",
URL = "http://www.stat.sc.edu/~ogden/papers/notpow2.ps",
}
@PhdThesis{ogd:thesis,
title = "Wavelet Thresholding in Nonparametric Regression with
Change-Point Applications",
author = "R. Todd Ogden",
school = "Texas A\&M University",
year = "1994",
postscript = "http://www.stat.sc.edu/~ogden/diss.ps",
}
@Article{ohs-iji-kur:online,
title = "Online detection of pulse sequence in random noise
using a wavelet",
author = "Ohsumi, A and Ijima, H. and Kuroishi, T",
journal = IEEETSP,
volume = "47",
number = "9",
pages = "2526--2531",
year = "1999",
abstract = "Two types of wavelet-based algorithms are proposed
for an online detection of a train of unknown pulse
signals corrupted by random noise. The mechanism of
detecting singularities hidden in the noisy
observation data is analyzed, and the performance of
the proposed signal detectors is
evaluated. Simulation studies are provided to
confirm the effectiveness of the algorithms."
}
@Unpublished{omb-etal:automatic,
title = "Automatic Statistical Analysis of Bivariate
Non-Stationary Time Series",
author = "Hernando C. Ombao and Jonathan A. Raz and Rainer
{von Sachs} and Beth A. Malow",
year = "1999",
note = "Submitted to {\em JASA}",
}
@Article{oon:detecting,
title = "A Wavelet Method for Detecting S-Waves in Seismic
Data",
author = "P. J. Oonicnx",
journal = "Computational Geosciences",
volume = "3",
pages = "111--134",
year = "1999",
}
@Article{pan-fan:wavelet-spectrum,
title = "Discrete wavelet transform power spectrum estimator",
author = "Jes{\'u}s Pando and Li-Zhi Fang",
journal = PRE,
volume = "57",
number = "3",
year = "1998",
pages = "3593--3601",
URL = "http://ojps.aip.org/PLEEE8-bt/html/57_3.html",
keywords = "nucleus-nucleus collisions high-energies
distributions fluctuations turbulence",
abstract = "A method for measuring the spectrum of a density
field by the discrete wavelet transform (DWT) is
studied. We show how the Fourier power spectrum can
be detected by using the wavelet function
coefficients (WFC) of the DWT. This method can
successfully measure the power spectrum in samples
for which traditional methods often fail because the
samples are finite sized, have a complex geometry,
or are varyingly sampled. We demonstrate that the
spectrum features, such as the power law index, the
magnitude, and the typical scales can be determined
by the DWT reconstructed spectrum. We apply this
method to analyze the power spectrum of the spatial
distribution of the Ly-alpha clouds. The two popular
data sets used for the spectrum detection have quite
different geometries and samplings, yet the
one-dimensional (1D) power spectra and their 3D
reconstruction given by the DWT estimator show the
same features. The analysis makes clear that the DWT
estimator is a sensitive tool in revealing common
and physical properties from diverse data sets.",
}
@Article{pan-muk:tidal,
title = "Wavelet analysis on transient behaviour of tidal
amplitude fluctuations observed by meteor radar in
the lower thermosphere above Bulgaria",
author = "Pancheva, D. and Mukhtarov, P.",
journal = AG,
volume = "18",
number = "3",
year = "2000",
pages = "316--331",
keywords = "Meteorology and atmospheric dynamics (middle
atmosphere dynamics; waves and tides) - Radio
science (nonlinear phenomena)"
abstract = "On the basis of bispectral analysis applied to the
hourly data set of neutral wind measured by meteor
radar: in the MLT region above Bulgaria it was
demonstrated that nonlinear processes are frequently
and regularly acting in the mesopause region. They
contribute significantly to the short-term tidal
variability and are apparently responsible for the
observed complicated behavior of the tidal
characteristics. A Morlet wavelet transform is
proposed as a technique for studying nonstationary
signals. By simulated data it. was revealed that the
Morlet wavelet transform is especially convenient
for analyzing signals with: (I) a wide range of
dominant frequencies which are-localized in
different time intervals; (2) amplitude and
frequency modulated spectral components, and (3)
singular, wavelike events, observed in the neutral
wind of the MLT region and connected mainly with
large-scale disturbances propagated from below. By
applying a Morlet wavelet transform to the hourly
values of the amplitudes of diurnal and
semidiurnal tides the basic oscillations with
periods of planetary waves (1.5-20 days), as well as
their development in time, are obtained. A
cross-wavelet analysis is used to clarify the
relation between the tidal and mean neutral wind
variability. The results of bispectral analysis
indicate: which planetary waves participated in the
nonlinear coupling with the atmospheric tides, while
the results of cross-wavelet analysis outline their
time intervals if these interactions are local.",
}
@Article{pan-wan:stochastic,
title = "A Stochastic Nonlinear Regression Estimator Using
Wavelets",
author = "Pan, Zuohong and Wang, Xiaodi",
journal = CE,
volume = "11",
number = "1-2",
year = "1998",
pages = "89--102",
keywords = "capital markets empirical studies including
regulation",
abstract = "A new wavelet-based estimator is introduced which
combines the state-space model with the wavelet
transform in an effort to explore the stock market
inefficiency. The new estimator possesses some
superior qualities that are illustrated through its
actual performance in forecasting the S&P 500.",
}
@Article{pap-sik-wei:characterization,
title = "The characterization of low pass filters and some
basic properties of wavelets, scaling functions and
related concepts",
author = "Papadakis, M. and \v{S}iki\'{c}, H. and Weiss, G.",
journal = JFAA,
volume = "5",
number = "5",
year = "1999",
pages = "495--521",
abstract = "The ``classical'' wavelets, those psi is an element
of L-2(R) such that {2(j/2)psi(2(j)x - k)}, j, k is
an element of Z, is an orthonormal basis for L-2(R),
are known to be characterized by two simple
equations satisfied by <(psi)over cap>. The
``multiresolution analysis'' wavelets (briefly, the
MRA wavelets) have a simple characterization and so
do the scaling functions that produce these
wavelets. Only certain smooth classes of the low
pass filters that are determined by these scaling
functions, however, appear to be characterized in
the literature (see Chapter 7 of [3] for an account
of these matters). In this paper we present a
complete characterization of all these filters. This
somewhat technical result does provide a method for
simple constructions of low pass filters whose only
smoothness assumption is a Holder condition at the
origin. We also obtain a characterization of all
scaling sets and, in particular a description of all
bounded scaling sets as well as a detailed
description of the class of scaling functions.",
}
@InProceedings{pap-sol-was:segmentation,
title = "Segmentation-independent estimates of turbulence
parameters",
author = "G. C. Papanicolaou and Knut S{\o}lna and Donald
C. Washburn",
booktitle = "Airborne Laser Advanced Technology",
editor = "T. D. Steiner and P. H. Merritt",
series = "Proceedings of the SPIE",
volume = "3381",
pages = "256--267",
year = "1998",
URL = "ftp://math.Stanford.EDU/pub/papers/papanicolaou/maint.ps.gz",
abstract = "We present a new approach for analyzing local power
law processes and apply it to temperature
measurements from the upper atmosphere. We segment
the data and use the wavelet scale spectrum to
estimate the parameters of the power law, the scale
factor and the exponent. These parameters vary from
segment to segment. Part of this variation is due to
the non-stationary of the data. Another part is due
to estimation errors that depend on the
segmentation. In this paper show how to remove
effectively these segmentation dependent
variations.",
}
@Unpublished{pap-sol:local,
title = "Wavelet based estimation of local {K}olmogorov
turbulence",
author = "G. Papanicolaou and K. S{\o}lna",
year = "1999",
URL = "ftp://math.Stanford.EDU/pub/papers/papanicolaou/main.ps.gz",
note = "Submitted to the {\em Journal of the American
Statistical Association}",
}
@Article{par-man:interannual,
title = "Interannual Temperature Events and Shifts in Global
Temperature: A ``Multiwavelet'' Correlation
Approach",
author = "Jeffrey Park and Michael E. Mann",
journal = EI,
volume = "4",
year = "2000",
pages = "???--???",
}
@InProceedings{pat-sim:texture,
title = "Texture modelling and synthesis using joint
statistics of complex wavelet coefficients",
author = "J. Portilla and E. P. Simoncelli",
booktitle = "IEEE Workshop on Statistical and Computational
Theories of Vision",
year = "1999",
pages = "",
URL = "ftp://ftp.cns.nyu.edu/pub/eero/portilla99a.ps.gz",
abstract = "We present a statistical characterization of texture
images in the context of an overcomplete complex
wavelet transform. The characterization is based on
empirical observations of statistical regularities
in such images, and parameterized by (1) the local
auto-correlation of the coefficients in each
subband; (2) both the local auto-correlation and
cross-correlation of coefficient magnitudes at other
orientations and spatial scales; and (3) the first
few moments of the image pixel histogram. We develop
an efficient algorithm for synthesizing random
images subject to these constraints using alternated
projections, and demonstrate its effectiveness on a
wide range of synthetic and natural textures. In
particular, we show that many important structural
elements in textures (e.g., edges, repeated patterns
or alternated patches of simpler texture), can be
captured through joint second order statistics of
the coefficient magnitudes. We also show the
flexibility of the representation, by applying to a
variety of tasks which can be viewed as constrained
image synthesis problems, such as spatial and
spectral extrapolation.",
}
@TechReport{pen-vid:non-equally,
title = "On non-equally spaced wavelet regression",
author = "Marianna Pensky and Brani Vidakovic",
number = "98-06",
institution = "Institute of Statistics and Decision Sciences, Duke
University",
year = "1998",
URL = "ftp://ftp.isds.duke.edu/pub/WorkingPapers/98-06.ps",
abstract = "Wavelet-based regression analysis is widely used
mostly for equally-spaced designs. For such designs
wavelets are superior to other traditional orthonormal
bases because of their versatility and ability to
parsimoniously describe irregular functions. If the
regression design is random, an automatic solution is
not available. Given the observations (X_i, Y_i), i =
1,..., n, we estimate the regression function
m(x)=E(Y|X=x) as a series \sum_k \hat c_{jk}
\phi_{jk}(x) where \{ \phi_{jk}(x), ~k \in Z \} are
scaling functions spanning the multiresolution subspace
V_j. We propose a method that utilizes a probabilistic
model on X_i's in defining the empirical coefficients
\hat c_{jk}. The paper deals with both theoretical and
practical aspects of the proposed estimator. We explore
MSE convergence rates of the estimator. The performance
of the estimator is compared to that of some
traditional regression methods.",
}
@TechReport{per-bru:approximate,
title = "Wavelet-Based Approximate Maximum Likelihood
Estimation for Trend-Contaminated Fractional
Difference Processes",
author = "Donald B. Percival and Andrew G. Bruce",
number = "67",
institution = "MathSoft, Inc., 1700 Westlake Avenue N., Seattle, WA
98109-9891",
year = "1998",
URL = "ftp://ftp.statsci.com/pub/longmem/wavelet-mle.ps",
}
@TechReport{per-bru:estimation,
title = "Estimation of Long Memory Processes with Missing
Data",
author = "Donald B. Percival and Andrew G. Bruce",
number = "64",
institution = "MathSoft, Inc., 1700 Westlake Avenue N., Seattle, WA
98109-9891",
year = "1997",
URL = "ftp://ftp.statsci.com/pub/longmem/missing.ps",
}
@Unpublished{per-sar-dav:wavestrapping,
title = "Wavestrapping Time Series: {A}daptive Wavelet-Based
Bootstrapping",
author = "Donald B. Percival and Sylvain Sardy and Anthony
Davision",
year = "1999",
note = "Isaac Newton Institute for Mathematical Sciences",
}
@InCollection{per-gut:introduction,
title = "An Introduction to Spectral Analysis and Wavelets",
author = "Donald B. Percival and Peter Guttorp",
pages = "175--186",
crossref = "cia-cox-mon-pav:advanced",
URL = "",
abstract = "",
}
@InCollection{per-gut:long-memory,
title = "Long-Memory Processes, the {A}llan Variance and
Wavelets",
author = "Donald B. Percival and Peter Guttorp",
pages = "325--344",
crossref = "fou-kum:geophysics",
URL = "",
abstract = "",
}
@Article{per-mof:subtidal,
title = "Analysis of Subtidal Coastal Sea Level Fluctuations
Using Wavelets",
author = "Donald B. Percival and Harold O. Mofjeld",
journal = JASA,
volume = "92",
number = "439",
year = "1997",
pages = "868--880",
keywords = "coastal sea level variability, discrete wavelet
transform, natural hazards, time series analysis,
tsunamis",
abstract = "Subtidal coastal sea level fluctuations affect coastal
ecosystems and the consequences of destructive events
such as tsunamis. We analyze a time series of subtidal
fluctuations at Crescent City, California, during
1980-1991 using the maximal overlap discrete wavelet
transform (MODWT). Our analysis shows that the
variability in these fluctuations depends on the season
for scales of 32 days and less. We show how the MODWT
characterizes nonstationary behavior succinctly and how
this characterization can be used to improve forecasts
of inundation during tsunamis and storm surges. Pie
provide pseudocode and enough details so that data
analysts in other disciplines can readily apply MODWT
analysis to other nonstationary time series.",
}
@Article{per-phi-bas:compared,
title = "Wavelet spectra compared to {F}ourier spectra",
author = "Val\'{e}rie Perrier and Thierry Philipovitch and
Claude Basdevant",
journal = "Journal of Mathematical Physics",
volume = "36",
number = "3",
year = "1995",
pages = "1506-1519",
abstract = "The relation between Fourier spectra and spectra
obtained from wavelet analysis is established. Small
scale asymptotic analysis shows that the wavelet spectrum
is meaningful only when the analyzing wavelet has enough
vanishing moments. These results are related to regularity
theorems in Besov spaces. For the analysis of infinitely
regular signals, a new wavelet, with an infinite number of
cancellations is proposed.",
}
@Book{per-wal:wmtsa,
title = "Wavelet Methods for Time Series Analysis",
author = "Donald B. Percival and Andrew T. Walden",
year = "2000",
publisher = "Cambridge University Press",
address = "Cambridge",
ISBN = "",
keywords = "",
URL = "http://weber.u.washington.edu/~dbp/",
abstract = "",
note = "Forthcoming",
}
@Article{per:characterization,
title = "{C}haracterization of frequency stability:
frequency-domain estimation of stability measures",
journal = PIEEE,
volume = "79",
number = "7",
year = "1991",
pages = "961--972",
author = "Donald B. Percival",
abstract = "The author focuses on the frequency domain approach,
which provides a complete characterization of
frequency. The standard characterization of frequency
stability in the frequency domain is the spectral
density function (SDF). The author describes SDFs that
model sampled frequency stability data and that are
related to the SDFs of the standard characterization.
On the basis of standard techniques in spectral
analysis, he outlines a systematic way of estimating
SDFs typical of frequency stability data. The
recommended procedure is to check for broadband bias in
the periodogram using a sequence of data tapers and, if
bias is in evidence, to design an autoregressive
prewhitening filter to prewhiten the data. The author
considers the relationship between the Allan variance
and the SDF and outlines two nonparametric ways of
translating stability measures between the two
domains-one based upon pilot analysis and the other
upon J. Rutman's bandpass variance (1978).",
keywords = "frequency stability. frequency domain. spectral
density function. spectral analysis. broadband bias.
periodogram. sequence of data tapers. autoregressive
prewhitening filter. Allan variance. pilot analysis.
bandpass variance.",
}
@Article{per:variance,
title = "On estimation of the wavelet variance",
author = "Donald B. Percival",
journal = BKA,
volume = "82",
number = "3",
year = "1995",
pages = "619--631",
URL = "ftp://ftp.statsci.com/pub/WAVELETS/papers/wavevar.ps.gz",
abstract = "Thw wavelet variance decomposes the variance of a time
series into components associated with differen scales.
We consider two estimators of the wavelet variance: the
first based upon the discrete wavelet transform, and
the second, called the maximal-overlap estimator, based
upon a filtering interpretation of wavelets. We
determine the large sample distribution for both
estimatorsand show that the maximal-overlap estimator
ismore efficient for a class of processes of interest
in the physical sciences. We discuss methods for
determining an approximate confidence interval for the
wavelet variance. We demonstrate through Monte Carlo
experiments that the large sample distribution for the
maximal-overlap estimator is a reasonable approximation
even for the moderate sample size of 128 observations.
We apply our proposed methodology to a series of
observations related to vertical shear in the ocean.",
}
@Article{pes-kri-car:time-invariant,
title = "Time-invariant orthonormal wavelet representations",
author = "Jean-Christophe Pesquet and Hamid Krim and Herv{\'e}
Carfantan",
journal = IEEETSP,
volume = "44",
number = "8",
year = "1996",
pages = "1964--1970",
abstract = "A simple construction of an orthonormal basis starting
with a so-called mother wavelet, together with an
efficient implementation gained the wavelet
decomposition easy acceptanceand generated a great
research interest in its applications. An orthonormal
basis may not, however, always be a suitable
representation of a signal, particularly when time (or
space) invariance is a required property. The
conventional way around this problem is to use a
redundant decomposition. We address the time-invariance
problem for orthonormal wavelet transforms and propose
an extension to wavelet packet decompositions. We show
that it,is possible to achieve time invariance and
preserve the orthonormality. We subsequently propose an
efficient approach to obtain such a decomposition. We
demonstrate the importance of our method by considering
some application examples in signal reconstruction and
time delay estimation.",
}
@InProceedings{pes-kri-lep-ham:bayesian,
title = "{B}ayesian approach to best basis selection",
booktitle = "IEEE International Conference on Acoustics, Speech,
and Signal Processing",
volume = "5",
year = "1996",
pages = "2634--2637",
author = "J. C. Pesquet and H. Krim and D. Leporini and E.
Hamman",
note = "7-10 May 1996, Atlanta, GA, USA",
abstract = "Wavelet packets and local trigonometric bases provide
an efficient framework and fast algorithms to obtain a
`best basis' or `best representation' of deterministic
signals. Applying these deterministic techniques to
stochastic processes may, however, lead to variable
results. We revisit this problem and introduce a prior
model on the underlying signal in noise and account for
the contaminating noise model as well. We thus develop
a Bayesian-based approach to the best basis problem,
while preserving the classical tree search
efficiency.",
keywords = "deterministic signals, Bayesian approach, wavelet
packets, local trigonometric bases, fast algorithms,
best basis selection, best signal representation,
deterministic techniques, stochastic processes,
stochastic signals, contaminating noise model,
classical tree search efficiency, Bernoulli-Gaussian
mixtures, Bernoulli-Gaussian priors",
}
@Article{pes:statistical,
title = "Statistical properties of the wavelet decomposition
of certain non-{G}aussian self-similar processes",
author = "Pesquet-Popescu B.",
journal = SP,
volume = "75",
number = "3",
pages = "303--322",
year = "1999",
email = "bpopescu@csi.com",
URL = "http://www.elsevier.nl/cas/tree/store/sigpro/sub/1999/75/3/1386.pdf",
keywords = "non-stationary signals self-similarity wavelet
analysis higher-order statistics alpha-stable
processes lower-order statistics long-range
dependence",
abstract = "Self-similar processes have recently received
increasing attention in the signal processing
community, due to their wide applicability in
modeling natural phenomena which exhibit ``1/f''
spectra and/or long-range dependence. At the same
time, wavelet decomposition has become a very useful
tool in describing nonstationary self-similar
processes. In this paper, we consider extensions of
existing results to non-Gaussian self-similar
processes. We first investigate the existence and
properties of higher-order statistics of wavelet
decomposition for self-similar processes with finite
variance. We then consider certain self-similar
processes with infinite variance, and study the
statistical properties of their wavelet
coefficients.",
}
@InProceedings{pet-ben:uranus,
title = "A New Insight in {U}ranus Rings: {A} Wavelet Analysis
of the {V}oyager 2 Data",
author = "J. M. Petit and Ph. Bendjoya",
booktitle = "Completing the Inventory of the Solar System",
editor = "Terrence W. Rettig and Joseph M. Hahn",
volume = "107",
series = "Astronomical Society of the Pacific Conference
Proceedings",
pages = "137--146",
year = "1996",
keywords = "wavelet analysis, uranus rings",
abstract = "A new signal processing analysis, based on the wavelet
transform has been developed. It allows the detection
and the reconstruction of fine structures in a very
noisy signal. It removes the noise and gives a
quantified level of detection of the structures against
chance fluctuations. This powerful method has been
applied on the PPS Voyager 2 data on the Uranus rings.
A preliminary catalog of structures found in the
$\sigma$ Sagitarii occultation experiment, is proposed
here.",
}
@TechReport{pet-ste:gamma,
title = "{EDF} statistics for testing for the {G}amma
distribution",
author = "N. A. Pettitt and M. A. Stephens",
institution = "Department of Statistics, Stanford University",
number = "323",
year = "1982",
}
@TechReport{pet:bayesian,
title = "Bayesian Spectral Analysis of Long Memory Time
Series",
author = "Giovanni Petris",
number = "97-08",
institution = "Institute of Statistics and Decision Sciences, Duke
University",
year = "1997",
URL = "ftp://ftp.isds.duke.edu/pub/WorkingPapers/97-08.ps",
}
@Article{pet:non-parametric,
title = "A non-parametric approach to the change point
problem",
author = "N. A. Pettitt",
journal = AS,
volume = "28",
number = "",
year = "1979",
pages = "126--135",
}
@Article{pet:some,
title = "Some results on estimating a change-point using
non-parametric type statistics",
author = "N. A. Pettitt",
journal = JSCS,
volume = "11",
number = "",
year = "1980",
pages = "261--272",
}
@PhdThesis{pet:thesis,
title = "Bayesian Analysis of Long Memory Time Series",
author = "Giovanni Petris",
year = "1997",
school = "Institute of Statistics and Decision Sciences, Duke
University",
postscript = "ftp://ftp.isds.duke.edu/pub/Theses/giovanni.ps.gz",
}
@Book{pie-etal:quadpack,
title = "\nobreak{QUADPACK}: A Subroutine Package for
Automatic Integration",
booktitle = "\nobreak{QUADPACK}: A Subroutine Package for
Automatic Integration",
author = "R. Piessons and E. {de Doncker-Kapenga} and
C. W. {\"U}berhuber and D. K. Kahaner",
series = "Springer Series in Computational Mathematics",
volume = "1",
publisher = "Springer-Verlag",
address = "Heidelberg",
year = "1983",
}
@Article{pin-vid:estimating,
title = "Estimating the square root of a density via compactly
supported wavelets",
author = "A. Pinheiro and B. Vidakovic",
journal = CSDA,
volume = "25",
number = "4",
year = "1997",
pages = "399--415",
}
@InCollection{plo-str:from,
title = "From Wavelets to Multiwavelets",
author = "Gerlind Plonka and Vasily Strela",
booktitle = "Mathamatical Methods for Curves and Surfaces II",
editor = "M. Dahlem and T. Lyche and L. Shumaker",
publisher = "Vanderbilt University Press",
year = "1998",
}
@Book{pre-teu-vet-fla:numerical,
title = "Numerical Recipes in {C}: The Art of Scientific
Computing",
author = "William H. Press and Saul A. Teukolsky and William T.
Vetterling and Brian P. Flannery",
edition = "2",
year = "1992",
publisher = "Cambridge University Press",
address = "Cambridge",
URL = "http://cfata2.harvard.edu/nr/",
}
@Article{pri:wavelets,
title = "Wavelets and Time-Dependent Spectral Analysis",
author = "M. B. Priestley",
journal = JTSA,
volume = "17",
number = "1",
year = "1996",
pages = "85--104",
abstract = "One of the key features of wavelet analysis is its
potential use for effecting time-frequency
decompositions of non-stationary signals. The
relationship between wavelet analysis and timedependent
spectral analysis has so far rested mainly on heuristic
reasoning: in this paper we examine the relationship in
a more precise mathematical form. A crucial feature of
this analysis is the need to define carefully the
notion of `frequency' when applied to non-stationary
signals.",
keywords = "Wavelets wavelet transforms discrete wavelet
transforms multiresolution analysis Fourier transforms
windowed Fourier transforms spectral analysis
uncertainty principle evolutionary spectra",
}
@InProceedings{pro-smi:multichannel,
title = "Multichannel time-series modelling and prediction by
wavelet networks",
author = "Ale\v{s} Proch{\'a}zka and Jonathan Smith",
booktitle = "VIII European Signal Processing Conference
EUSIPCO-96",
year = "1996",
pages = "???--???",
URL = "http://rex.vscht.cz/prochaz/ps/eusip96.ps",
}
@Article{pro-vei:trends,
title = "Trends, cycles and nonstationarities in isotope
signals of {P}hanerozoic seawater",
author = "Prokoph, A. and Veizer, J.",
journal = CG,
volume = "161",
number = "1-3",
year = "1999",
pages = "225--240",
abstract = "The new set of Sr-87/Sr-86, delta(18)O and
delta(13)C experimental data for Phanerozoic
seawater, the ``Bochum/Ottawa Isotope Dataset'', has
been tested by wavelet, discontinuity and sliding
window correlation dimension analyses for
cyclicities and nonstationarities in the isotope
signal. The tests indicate discontinuities in the
strontium isotope signal at similar to 500, 340,
288, 210, 65 and 28 Ma, while for the oxygen and
carbon isotopes they are at similar to 500, 385,
290, 210 and 65 Ma. These discontinuities, often
coincident with major stage boundaries, reflect
mostly single (likely tectonic) events that do not
affect the structure of the underlying system. The
two most pronounced nonstationarities in all isotope
systematics are at similar to 65 and 210 Ma,
respectively, that is at the K/T and Norian/Rhaetian
transitions. Wavelet analysis for all three isotope
systems yields a long-term quasi-periodicity at
similar to 94-125 Ma, best developed during the
Paleozoic, with superimposed intermittent 48-57 and
29-35 Ma oscillations, all likely a reflection of
plate reorganizations within the Caledonian,
Hercynian and Alpine tectonic cycles.",
}
@Article{qiu-er:wavspect,
title = "Wavelet spectrogram of noisy signals",
author = "Lunji Qiu and Meng Hwa Er",
journal = IJE,
volume = "79",
number = "5",
year = "1995",
pages = "665--677",
email = "elqiu@ntuvax.ntu.ac.sg",
abstract = "The wavelet transform is of interest for analysing
non- stationary signals. The squared modulus of the
wavelet transform leads to the wavelet spectrogram or
scalogram. When signals are embedded in additive noise,
it is important to study the estimation accuracy in
terms of bias and variance. The mean and variance
statistical properties of the wavelet spectrogram of a
signal embedded in additive gaussian white noise are
derived in this paper. Examples and simulation results
are also presented.",
}
@Article{qiu-u-sha:leakeage,
title = "The leakage problem of orthonormal wavelet
transforms when applied to atmospheric turbulence",
author = "Jie Qiu and Kyaw Tha Paw U and Roger H. Shaw",
journal = JGRA,
volume = "100",
number = "D12",
year = "1995",
pages = "25,769--25,779",
abstract = "Orthonormal wavelet transforms are becoming common
in the study of turbulence phenomena. Although they
are powerful tools in representing a signal, their
use as tools to study the characteristics of
turbulent structures can create appreciable errors
in interpretation. It is shown here that although
the orthonormal wavelet transform is computationally
economical by taking advantage of multiresolution
analysis, it has insufficient resolution in both
scale and location to resolve detailed information
of turbulence structures. Lacking in resolution, the
energy at a particular frequency (or wavelength) may
leak into neighboring frequencies and may pass down
to smaller scales to produce an artificial
``cascade'' of energy (with a slope close to
-2/3). The choice of wavelet basis function is
important to the wavelet spectrum, especially in the
study of turbulence flows dominated by coherent
structures, since the method most accurately senses
energy contained in pulses that have a similar
pattern to the wavelet function. To use the method
as a filter can be problematic owing to the low
resolution of the orthonormal wavelet transform;
nonorthonormal wavelet analysis should be employed
when high resolution is important. When orthonormal
wavelet transforms have to be used for signal
analysis, segmented averaging should be employed.",
}
@Book{rai:book,
title = "Special Functions",
author = "Earl D. Rainville",
year = "1960",
publisher = "The Macmillan Company",
address = NY,
}
@Article{rai:minimax,
title = "Minimax estimation of sharp change points",
author = "Raimondo, M.",
journal = AofS,
volume = "26",
number = "4",
year = "1998",
pages = "1379--1397",
keywords = "change point cusp jump minimax estimation
nonparametric regression wavelets",
abstract = "We define the sharp change point problem as an
extension of earlier problems in change point
analysis related to nonparametric regression. As
particular cases, these include estimation of jump
points in smooth curves. More generally, we give a
systematic treatment of the correct rate of
convergence for estimating the position of a `cusp'
of an arbitrary order. We propose a test function
for the local regularity of a signal sample
implementation of our method, from observations of
the signal at discrete time positions i/n, i =
1,..., n, we use a wavelet transformation to
approximate the position of the change point in the
no-noise case. We study the noise effect, in the
worst case scenario over a wide class of functions
having a unique irregularity of `order alpha' and
propose a sequence of estimators which converge at
the rate n(-1/(1+2 alpha)), as n tends to
infinity. Finally we analyze the likelihood ratio of
the problem and show that this is actually the
minimax rate of convergence. Examples of
thresholding empirical wavelet coefficients to
estimate the position of sharp change points are
also presented.",
}
@Article{ram-lam:decomposition,
title = "Decomposition of economic relationships by timescale
using wavelets - {M}oney and income",
author = "Ramsey, J. B. and Lampart, C.",
journal = "Macroeconomic Dynamics",
volume = "2",
number = "1",
year = "1998",
pages = "49--71",
keywords = "wavelets timescale velocity money income permanent
income hypothesis money-income causality",
abstract = "Economists have long known that timescale matters in
that the structure of decisions as to the relevant
time horizon, degree of time aggregation, strength
of relationship, and even the relevant variables
differ by timescale. Unfortunately, until recently
it was difficult to decompose economic time series
into orthogonal timescale components except for the
shea or long run in which the former is dominated by
noise. Wavelets are used to produce an orthogonal
decomposition of some economic variables by
timescale over six different timescales. The
relationship of interest is that between money and
income, i.e., velocity. We confirm that timescale
decomposition is very important for analyzing
economic relationships. The analysis indicates the
importance of recognizing variations in phase
between variables when investigating the
relationships between them and throws considerable
light on the conflicting results that have been
obtained in the literature using Granger causality
tests.",
}
@Article{ram-lam:decomposition2,
title = "The Decomposition of economic relationships by time
scale using wavelets: {E}xpenditure and income",
author = "Ramsey, J. B. and Lampart, C.",
journal = "Studies in Nonlinear Dynamics and Econometrics",
volume = "3",
number = "1",
year = "1998",
pages = "23--42",
keywords = "permanent income consumption hypothesis",
abstract = "Economists have long known that time scale matters,
in that the structure of decisions as to the
relevant time horizon, degree of time aggregation,
strength of relationship, and even the relevant
variables differ by time scale. Unfortunately, until
recently it was difficult to decompose economic time
series into orthogonal time-scale components except
for the short and long run, in which the former is
dominated by noise. This paper uses wavelets to
produce an orthogonal decomposition of some economic
variables by time scale over six different time
scales. The relationship of interest is the
permanent income hypothesis. We confirm that
time-scale decomposition is very important for
analyzing economic relationships and that a number
of anomalies previously noted in the literature are
explained by these means. The analysis indicates the
importance of recognizing variations in phase
between variables when investigating the economic
relationships.",
}
@Article{ram-usi-zas:us-stock,
title = "An analysis of {U.S.} Stock Price Behavior Using
Wavelets",
author = "Ramsey, James B. and Uskinov, Daniel and Zaslavsky,
George M.",
journal = "Fractals",
volume = "3",
number = "2",
year = "1995",
pages = "377--389",
keywords = "",
abstract = "",
}
@Article{ram-zei:fBm,
title = "On the wavelet transform of fractional {B}rownian
motion",
author = "J. Ramanathan and O. Zeitouni",
journal = IEEETIT,
volume = "37",
number = "4",
year = "1991",
pages = "1156--1158",
keywords = "wavelet transform, fractional Brownian motion,
covariance structure, Gaussian processes",
abstract = "A theorem characterizing fractional Brownian motion by
the covariance structure of its wavelet transform is
established. The authors examine whether there are
alternate Gaussian processes whose wavelet transforms
have a natural covariance structure. In addition, the
authors examine if there are any Gaussian processes
whose wavelet transform is stationary with respect to
the affine group (i.e. the statistics of the wavelet
transform do not depend on translations and dilations
of the process).",
}
@Article{ram-zha:analysis,
title = "The analysis of foreign exchange data using waveform
dictionaries",
author = "James B. Ramsey and Zhifeng Zhang",
journal = "Journal of Empirical Finance",
volume = "4",
year = "1997",
pages = "341--372",
}
@InCollection{ram-zha:application,
title = "The application of wave form dictionaries to stock
market index data",
author = "Ramsey, J. B. and Zhang, Z. F.",
booktitle = "Predictability of Dynamical Systems",
editor = "Kravstov, Y. A. and Kadtke, J. B.",
publisher = "Springer Verlag",
address = NY,
volume = "69",
year = "1996",
pages = "189--205",
}
@Article{ram:contribution,
title = "The contribution of wavelets to the anlaysis of
economic and financial data",
author = "James B. Ramsey",
journal = PTRSLA,
volume = "357",
number = "1760",
year = "1999",
pages = "2593--2606",
}
@Unpublished{ram:regression,
title = "Regression over Time Scale Decompositions: {A}
Sampling Analysis of Distributional Properties",
author = "James B. Ramsey",
year = "1998",
note = "New York University",
}
@Article{rei-etal:multifractal,
title = "A multifractal wavelet model with application to
network traffic",
author = "Riedi, R. H. and Crouse, M. S. and Ribeiro,
V. J. and Baraniuk, R. G.",
journal = IEEETIT,
volume = "45",
number = "3",
year = "1999",
pages = "992--1018",
URL = "",
keywords = "long-range dependence multifractals network traffic
positive 1/f noise wavelets",
abstract = "In this paper, we develop a new multiscale modeling
framework for characterizing positive-valued data
with long-range-dependent correlations (1/f
noise). Using the Haar wavelet transform and a
special multiplicative structure on the wavelet and
scaling coefficients to ensure positive results, the
model provides a rapid O(N) cascade algorithm for
synthesizing N-point data sets. We study both the
second-order and multifractal properties of the
model, the latter after a tutorial overview of
multifractal analysis. We derive a scheme for
matching the model to real data observations and, to
demonstrate its effectiveness, apply the model to
network traffic synthesis. The flexibility and
accuracy of the model and fitting procedure result
in a close fit to the real data statistics
(variance-time plots and moment scaling) and queuing
behavior, Although for illustrative purposes we
focus on applications in network traffic modeling,
the multifractal wavelet model could be useful in a
number of other areas involving positive data,
including image processing, finance, and
geophysics.",
}
@InProceedings{rib-etal:simulating,
title = "Simulation of non{G}aussian Long-Range Dependent
Traffic using Wavelets",
author = "V. J. Ribeiro and R. H. Riedi and M. S. Crouse and
R. G. Baraniuk",
booktitle = "ACM SIGMETRICS Conference on the Measurement and
Modeling of Computer Systems",
year = "1999",
note = "1-4 May 1999, Atlanta, Georgia",
abstract = "In this paper, we develop a simple and powerful
multiscale model for the synthesis of nonGaussian,
long-range dependent (LRD) network traffic. Although
wavelets effectively decorrelate LRD data,
wavelet-based models have generally been restricted
by a Gaussianity assumption that can be unrealistic
for traffic. Using a multiplicative superstructure
on top of the Haar wavelet transform, we exploit the
decorrelating properties of wavelets while
simultaneously capturing the positivity and
``spikiness'' of nonGaussian traffic. This leads to
a swift O(N) algorithm for fitting and synthesizing
N-point data sets. The resulting model belongs to
the class of multifractal cascades, a set of
processes with rich statistical properties. We
elucidate our model's ability to capture the
covariance structure of real data and then fit it to
real traffic traces. Queueing experiments
demonstrate the accuracy of the model for matching
real data. Our results indicate that the nonGaussian
nature of traffic has a significant effect on
queuing.",
}
@Unpublished{rid-den:aeromagnetic,
title = "The wavelet transform in aeromagnetic processing",
author = "T. A. Ridsdill-Smith and M. C. Dentith",
journal = "GEOPHYSICS",
volume = "64",
number = "4",
year = "1999",
pages = "1067--1078",
URL = "http://geolpc42.geol.uwa.edu.au/papers/wavemag.zip",
abstract = "The phase-shift method of wavefield extrapolation
applies a phase shift in the Fourier domain to deduce
a scalar wavefield at one depth level given its value
at another. The phase-shift operator varies with
frequency and wavenumber, and assumes constant
velocity across the extrapolation step. We use
nonstationary filter theory to generalize this method
to nonstationary phase shift (NSPS), which allows the
phase shift to vary laterally depending upon the local
propagation velocity. For comparison, we derive an
analytic form for the popular phase shift plus
interpolation (PSPI) method in the limit of an
exhaustive set of reference velocities. NSPS and this
limiting form of PSPI can be written as generalized
Fourier integrals which reduce to ordinary phase shift
in the constant velocity limit. In the (x, omega)
domain, these processes are the transpose of each
other; however, only NSPS has the physical
interpretation of forming the scaled, linear
superposition of laterally-variable impulse responses
(i.e., Huygen's wavelets).The difference between NSPS
and PSPI is clear when they are compared in the case
of a piecewise constant velocity variation. Define a
set of windows such that the jth window is unity when
the propagation velocity is the jth distinct velocity
and is zero otherwise. NSPS can be computed by applying
the window set to the input data to create a set of
windowed wavefields, which are individually phase-shift
extrapolated with the corresponding constant velocity,
and the extrapolated set is superimposed. PSPI proceeds
by phase-shift extrapolating the input data for each
distinct velocity, applying the jth window to the jth
extrapolation, and superimposing. Though neither
process is fully correct, PSPI has the unphysical limit
that discontinuities in the lateral velocity variation
cause discontinuities in the wavefield, whereas NSPS
shows the expected wavefront ``healing.'' We then
formulate a finite aperture compensation for NSPS which
has the practical result of absorbing lateral boundaries
for all incidence angles. Wavefield extrapolation can be
regarded as the crosscorrelation of the wavefield with
the expected response of a point diffractor at the new
depth level. Aperture compensation simply applies a
laterally varying window to the infinite, theoretical
diffraction response. The crosscorrelation becomes
spatially variant, even for constant velocity, and hence
is a nonstationary filter. The nonstationary effects of
aperture compensation can be simultaneously applied with
the NSPS extrapolation through a laterally variable
velocity field.",
}
@Article{rid:separating,
title = "Separation filtering of aeromagnetic data using
filter-banks",
author = "T. A. Ridsdill-Smith",
journal = "Exploration Geophysics",
volume = "29",
number = "3-4",
year = "1998",
pages = "577--583",
URL = "http://geolpc42.geol.uwa.edu.au/papers/aseg98trs.zip",
abstract = "",
}
@Article{rie-sid:adaptive,
title = "Adaptive smoothing of the log-spectrum with multiple
tapering",
author = "Kurt S. Riedel and Alexander Sidorenko",
journal = IEEETSP,
volume = "44",
number = "7",
year = "1996",
pages = "1794--1800",
abstract = "A hybrid estimator of the log-spectral density of a
stationary time series is proposed, First, a multiple
taper estimate is performed, followed by kernel
smoothing the log-multiple taper estimate, This
procedure reduces the expected mean square error by
(pi(2)/4)(4/5) over simply smoothing the log tapered
periodogram, A data-adaptive implementation of a
variable-bandwidth kernel smoother is given.",
}
@Article{rie-etal:multifractal-wavelet,
title = "A Multifractal Wavelet Model with Application to
Network Traffic",
author = "R. H. Riedi and M. S. Crouse and V. J. Ribeiro and
R. G. Baraniuk",
journal = IEEETIT,
volume = "45",
number = "4",
year = "1999",
pages = "992--1018",
URL = "http://www-dsp.rice.edu/~riedi/cv_frame.html",
keywords = "Multifractals, long-range dependence, positive 1/f
noise, wavelets, network traffic",
abstract = "In this paper, we develop a new multiscale modeling
framework for characterizing positive-valued data
with long-range-dependent correlations (1/f
noise). Using the Haar wavelet transform and a
special multiplicative structure on the wavelet and
scaling coefficients to ensure positive results, the
model provides a rapid O(N) cascade algorithm for
synthesizing N-point data sets. We study both the
second-order and multifractal properties of the
model, the latter after a tutorial overview of
multifractal analysis. We derive a scheme for
matching the model to real data observations and, to
demonstrate its effectiveness, apply the model to
network traffic synthesis. The flexibility and
accuracy of the model and fitting procedure result
in a close fit to the real data statistics
(variance-time plots and moment scaling) and queuing
behavior. Although for illustrative purposes we
focus on applications in network traffic modeling,
the multifractal wavelet model could be useful in a
number of other areas involving positive data,
including image processing, finance, and
geophysics.",
}
@InProceedings{rie:geophysics,
title = "Multifractals and Wavelets: {A} potential tool in
Geophysics",
author = "R. H. Riedi",
booktitle = "Society of Exploration Geophysicists Annual Meeting",
address = "New Orleans",
year = "1998",
pages = "???--???",
URL = "http://www-dsp.rice.edu/~riedi/cv_frame.html",
}
@TechReport{rie:introduction,
title = "Introduction to Multifractals",
author = "R. H. Riedi",
number = "99-06",
institution = "ECE Department, Rice University",
year = "1999",
}
@Article{rio-fla:time-scale,
title = "Time-Scale Energy Distributions: {A} General Class
Extending Wavelet Transforms",
author = "Olivier Rioul and Patrick Flandrin",
journal = IEEETSP,
volume = "40",
number = "7",
year = "1992",
pages = "1746--1757",
abstract = "A proposed theoretical framework for time-scale energy
representation is based on local frequency which is
covariant under modulations and time scaling which is
covariant under dilations or contractions. The
frameworks seeks to illustrate the relationship between
scalograms and spectrograms. Results show that, from
the Wigner-Ville distribution, it is possible to shift
continuously to either a scalogram or a spectrogram.
The approach simultaneously maintains a balance between
time-frequency resolution and cross-terms reduction in
both time-scale and time-frequency representations.",
}
@Article{rio-vet:wavelets,
title = "Wavelets and Signal Processing",
author = "Olivier Rioul and Martin Vetterli",
journal = IEEESPM,
volume = "8",
number = "4",
year = "1991",
pages = "14--38",
abstract = "A simple, nonrigorous, synthetic view of wavelet
theory is presented for both review and tutorial
purposes. The discussion includes nonstationary signal
analysis, scale versus frequency, wavelet analysis and
synthesis, scalograms, wavelet frames and orthonormal
bases, the discrete-time case, and applications of
wavelets in signal processing. The main definitions and
properties of wavelet transforms are covered, and
connections among the various fields where results have
been developed are shown.",
}
@TechReport{rio-vid:random,
title = "Wavelet-Based Random Densities",
author = "David Insua Rios and Brani Vidakovi\'{c}",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
year = "1997",
note = "Discussion Paper 97-05",
URL = "ftp://ftp.isds.duke.edu/pub/WorkingPapers/97-05.ps",
}
@Article{rob-par-alv:extraction,
title = "Extraction of impulse response data via wavelet
transform for structural system identification",
author = "A. N. Robertson and K. C. Park and K. F. Alvin",
journal = JVA,
volume = "120",
number = "1",
year = "1998",
pages = "252--260",
keywords = "vibration",
abstract = "This paper presents a wavelet transform-based method
of extracting the impulse response characteristics from
the measured disturbances and response histories of
linear structural dynamic systems. The proposed method
is found to be effective in determining the impulse
response functions for systems subjected to harmonic
(narrow frequency-band) input signals and signals with
sharp discontinuities, thus alleviating the Gibbs
phenomenon encountered in FFT methods. When the system
is subjected to random burst input signals for which
the FFT methods are known to perform well, the proposed
wavelet method performs equally well with a fewer
number of ensembles than FFT-based methods. For
completely random input signals, both the wavelet and
FFT methods experience difficulties, although the
wavelet method appears to perform somewhat better in
tracing the fundamental response modes.",
}
@Article{rob-par-alv:identification,
title = "Identification of structural dynamics models using
wavelet-generated impulse response data",
author = "A. N. Robertson and K. C. Park and K. F. Alvin",
journal = JVA,
volume = "120",
number = "1",
year = "1998",
pages = "261--266",
keywords = "vibration",
abstract = "",
}
@InProceedings{rom-cho-bar:bayesian,
title = "{B}ayesian Tree-Structured Image Modeling using
Wavelet-domain Hidden {M}arkov Models",
author = "J. K. Romberg and H. Choi and R. G. Baraniuk",
booktitle = "SPIE Technical Conference on Mathematical Modeling,
Bayesian Estimation, and Inverse Problems",
volume = "3816",
year = "1999",
pages = "31--44",
email = "jrom@rice.edu, choi@ece.rice.edu, richb@rice.edu",
URL = "http://www-dsp.rice.edu/publications/pub/jrom99spie.ps.Z",
abstract = "Wavelet-domain hidden Markov models have proven to
be useful tools for statistical signal and image
processing. The hidden Markov tree model captures
the key features of the joint density of the wavelet
coefficients of real-world data. One potential
drawback to the HMT framework is the need for
computationally expensive iterative training. In
this paper, we prose two reduced-parameter HMT
models that capture the class of real-world
images. In the image HMT (iHMT) model we use the
fact that for a large class of images the structure
of the HMT is self-similar across scale. This allows
us to reduce the complexity of the iHMT to just nine
easily trained parameters. In the universal HMT
(uHMT) we take a Bayesian approach and fix these
nine parameters. The uHMT requires no training of
any kind. While simple, we show using a series of
image estimation/denoising experiments that these
two new models retain nearly all of the key
structure modeled by the full HMT. Finally, we
propose a fast shift-invariant HMT estimation
algorithm that outperforms all other wavelet- based
estimators in the current literature, both in mean-
square error and visual metrics.",
}
@InProceedings{rom-cho-bar:bayesian2,
title = "{B}ayesian Wavelet Domain Image Modeling using
Hidden {M}arkov Trees",
author = "J. K. Romberg and H. Choi and R. G. Baraniuk",
booktitle = "Proceedings of the IEEE International Conference on
Image Processing",
volume = "",
year = "1999",
pages = "???--???",
email = "jrom@rice.edu, choi@ece.rice.edu, richb@rice.edu",
URL = "http://www-dsp.rice.edu/publications/pub/jrom-icip99.ps.Z",
}
@InProceedings{rom-cho-bar:shift-invariant,
title = "Shift-Invariant Denoising using Wavelet-Domain
Hidden {M}arkov Trees",
author = "J. K. Romberg and H. Choi and R. G. Baraniuk",
booktitle = "Conference Record of The Thirty-Third Asilomar
Conference on Signals, Systems and Computers",
volume = "",
year = "1999",
pages = "???--???",
email = "jrom@rice.edu, choi@ece.rice.edu, richb@rice.edu",
URL = "http://www-dsp.rice.edu/publications/pub/jrom-asilomar99.ps.Z",
}
@Unpublished{rou-vei:measuring,
title = "Measuring Long-Range Dependence Under Changing
Traffic Conditions",
author = "Matthew Roughan and Darryl Veitch",
year = "1999",
note = "preprint",
}
@InProceedings{rou-vei-abr:on-line,
title = "On-line estimation of the parameters of long-range
dependence",
author = "Matthew Roughan and Darryl Veitch and Patrice Abry",
booktitle = "Proceedings Globecom '98",
address = "Sydney",
volume = "6",
year = "1998",
pages = "3716--3721",
}
@Article{rug-vid:bayesian,
title = "A Bayesian decision theoretic approach to the choice
of thresholding parameter",
author = "Ruggeri, F. and Vidakovic, B.",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "183--197",
keywords = "Bayes rule hard-thresholding wavelets",
abstract = "Thresholding rules recently became of considerable
interest when Donoho and Johnstone applied them in
the wavelet shrinkage context. Analytically simple,
such rules are very efficient in data denoising and
data compression problems. In this paper we find
hard thresholding decision rules that minimize Bayes
risk for broad classes of underlying
models. Standard Donoho-Johnstone test signals are
used to evaluate performance of such rules. We show
that an optimal Bayesian decision theoretic (BDT)
hard thresholding rule can achieve smaller mean
squared error than some standard wavelet
thresholding methods, if the prior information on
the noise level is precise.",
}
@Book{rus-etal:wavelets,
title = "Wavelets and Their Applications",
booktitle = "Wavelets and Their Applications",
editor = "Mary Beth Ruskai and Gregory Beylkin and Ronald
Coifman and Ingrid Daubechies and Stephane Mallat and
Yves Meyer and Louise Raphael",
publisher = "Jones and Bartlett Publishers",
year = "1992",
pages = "474",
URL = "http://www.jbpub.com/catalog/Detail.CFM?titles__ISBN=0867202254",
loc = "QA 403.3 .W385 1992",
ISBN = "0-86720-225-4",
}
@Article{rus-lab-les:commodity,
title = "Wavelet Analysis of Commodity Price Behavior",
author = "Davidson, Russell and Labys, Walter C. and Lesourd,
Jean-Baptiste",
journal = CE,
volume = "11",
number = "1-2",
year = "1998",
pages = "103--128",
abstract = "We propose a form of semi-nonparametric regression
based on wavelet analysis. Traditional time series
methods usually involve either the time or the
frequency domain, but wavelets can combine the
information from both of these. While wavelet
transforms are typically restricted to equally
spaced observations an integer power of 2 in number,
we show how to go beyond these constraints. We use
our methods to construct ``patios'' for twenty-one
important international commodity price
series. These graph the magnitude of the variations
in the series at different time scales for various
subperiods of the full sample.",
}
@Article{sac-pra:coherent,
title = "Coherent modes in multiscale variability of
streamflow over the {U}nited {S}tates",
author = "Saco, P. and Kumar, P.",
journal = WRR,
volume = "36",
number = "4",
year = "2000",
pages = "1049--1067",
URL = "",
abstract = "Motivated by the need to understand large-scale
hydrologic response, significant research has been
directed toward the identification of coherent
regions using characteristics of streamflow
variability. Typically, these regions are delineated
using principal component analysis on
streamflow. This method does not account for
differences in temporal scales of fluctuations
embedded in the time series. To capture this, we use
wavelet spectral analysis. Wavelet spectra from the
specific streamflow series are obtained for outflow
binned at 3 degrees-length segments along the border
of the conterminous United States. Rotated principal
component analysis is performed on the wavelet
spectra to obtain clusters of segments that exhibit
similar distribution of variability across
scales. Three physically distinct modes explain over
89% of the variability. Two of the modes identified
are associated with high variability at seasonal
scales, and the third is associated with high
variability at small timescales. The runoff
generation mechanisms underlying the observed modes
of multiscale variability of various regions are
also discussed. Each of these coherent modes of
multiscale variability indicate the existence of
regions with similar scales of fluctuations that are
located geographically apart, as well as regions
located geographically close with dissimilar scales
of fluctuations.",
}
@Article{sai-bey:autocorrelation,
title = "Multiresolution representations using the
autocorrelation functions of compactly supported
wavelets",
author = "Naoki Saito and Gregory Beylkin",
journal = IEEETSP,
volume = "41",
number = "12",
year = "1993",
pages = "3584--3590",
URL = "http://math.ucdavis.edu/~saito/publications/miniframe.html",
abstract = "Proposes a shift-invariant multiresolution
representation of signals or images using dilations
and translations of the autocorrelation functions of
compactly supported wavelets. Although these
functions do not form an orthonormal basis, their
properties make them useful for signal and image
analysis. Unlike wavelet-based orthonormal
representations, the present representation has (1)
symmetric analyzing functions, (2) shift-invariance,
(3) associated iterative interpolation schemes, and
(4) a simple algorithm for finding the locations of
the multiscale edges as zero-crossings. The authors
also develop a noniterative method for
reconstructing signals from their zero-crossings
(and slopes at these zero-crossings) in their
representation. This method reduces the
reconstruction problem to that of solving a system
of linear algebraic equations.",
}
@InProceedings{sai:asilomar98,
title = "The least statistically-dependent basis and its
applications",
author = "Naoki Saito",
booktitle = "Conference Record of The Thirty-Second Asilomar
Conference on Signals, Systems and Computers",
year = "1998",
pages = "732--736",
URL = "http://math.ucdavis.edu/~saito/publications/asilomar98.html",
}
@Unpublished{sai:image,
title = "Image approximation and modeling via least
statistically-dependent bases",
author = "Naoki Saito",
note = "Submitted to {\em Pattern Recognition}",
year = "1999",
abstract = "Statistical independence is one of the most desirable
properties of a coordinate system for representing and
modeling images. In reality, however, truly independent
coordinates may not exist for a given set of images, or
it may be too difficult to compute them in practice.
Therefore, it makes sense to obtain the least
statistically-dependent coordinate system efficiently.
To achieve this goal, we use the best-basis algorithm
with new criterion that can rapidly select the least
statistically-dependent basis (LSDB) from a basis
dictionary (e.g., the local cosine or wavelet packet
dictionaries) containing a huge number of orthonormal
(or biorthogonal) bases. Our new basis selection
criterion is minimization of the mutual information of
the distributions of the basis coefficients as a
measure of statistical dependence, which in turn is
equivalent to minimization of the sum of the
differential entropy of each coordinate in the basis
dictionary. We show that this criterion, combined with
the best-basis algorithm, can find the coordinates
closest to the statistical independence from all
possible bases searchable in a basis dictionary with
O(n [log n]^p), where n is the dimensionality of the
image (the number of pixels in each image), and p=1 for
the wavelet packet dictionaries, and p=2 for the local
cosine/sine dictionaries. In this sense, we can view
this LSDB algorithm as the best-basis version of the
Independent Component Analysis (ICA), which is
increasingly gaining popularity. This criterion is
different from that of the Joint Best Basis (JBB)
proposed by Wickerhauser, which can be viewed as the
best-basis version of the Karhunen-Loeve basis (KLB).
We demonstrate the application of the LSDB to image
approximation and modeling and compare its performance
with that of KLB and JBB using a collection of real
geophysical acoustic waveforms and an image database
of human faces. For these datasets, the LSDB provides
the best approximation in terms of the average relative
l^2 errors among various bases including the KLB, JBB,
DCT, and wavelet basis. For image modeling, we propose
two simple stochastic models for a given class of
signals or images based on the LSDB coordinates. The
first model is to assume the statistical independence
among the LSDB coordinates, which allows us to sample
typical coefficients of each coordinate separately
using the empirical distribution estimated from the
available training coefficients of that coordinate,
which in turn easily allows us to simulate new images
at our disposal. For the geophysical acoustic
waveforms, this first model turned out to be good
enough. The second model is based on the ``second
rotation'' by the KLB computed from the top m LSDB
coordinates. This model gives us the decorrelated
coordinates built on top of the LSDB coordinates.
The simulation results on the human face database
using the second model suggest that this second
rotation can further reduce the statistical
dependency among the coordinates, and allows better
modeling for a class of complicated images.",
}
@InProceedings{sai:least,
title = "Least statistically-dependent basis and its
applications to image modeling",
author = "Naoki Saito",
pages = "24--37",
crossref = "lai-uns-ald:wavelet6",
URL = "http://math.ucdavis.edu/~saito/publications/lsdb_spie2.html",
}
@PhdThesis{sai:thesis,
title = "Local Feature Extraction and Its Applications Using a
Library of Bases",
author = "Naoki Saito",
school = "Yale University",
year = "1994",
URL = "http://math.ucdavis.edu/~saito/publications/saito_phd.html",
}
@Article{sak:pseudo,
title = "Pseudodiagonalization of the autocorrelation of a
stochastic process by an over-complete wavelet system",
author = "F. Sakaguchi",
journal = ECJ3,
volume = "78",
number = "4",
year = "1995",
pages = "16--27",
note = "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
Vol. 77-A, No. 8, August 1994, pp. 1065--1074",
abstract = "If a stochastic process can be regarded as a
superposition of the wavelets which arise randomly and
independently of one another, the random-wavelet
picture of a stochastic process is intuitive and
convenient. This paper investigates theoretically in
what case the picture can be used; i.e., in what case
the autocorrelation of the stochastic process can be
diagonalized by using the over-complete wavelet system.
A general method for calculating the pseudodiagonal
form from an arbitrarily given autocorrelation function
using the operator algebra is proposed. Next, some
properties of stationary wavelet-diagonal processes are
investigated where it is shown that the power spectra
of these processes are related to the spectral
estimates under the circumstances in which the number
of the time points are constrained to a constant finite
number.",
}
@Article{sar-brz:shift-invariant,
title = "A Shift-Invariant Discrete Wavelet Transform",
author = "Hamed Sari-Sarraf and Dragana Brzakovic",
journal = IEEETSP,
volume = "45",
number = "10",
year = "1997",
pages = "2621--2626",
abstract = "This correspondence presents a unifying approach to
the derivation and implementation of a shift-invariant
wavelet transform of one-and two-dimensional (1-D and
2-D) discrete signals, Starting with Mallat's
multiresolution wavelet representation (MRWAR), the
correspondence presents an analytical process through
which a shift-invariant, orthogonal, discrete wavelet
transform called the multiscale wavelet representation
(MSWAR) is obtained, The coefficients in MSWAR are
shown to be inclusive of those in MRWAR with the
implication that the derived representation is
invertible. The computational complexity of MSWAR is
quantified in terms of the required convolutions, and
its implementation is shown to be equivalent to the
filter upsampling technique.",
}
@Article{sar-etal:unequal,
title = "Wavelet DeNoising for Unequally Spaced Data",
author = "Sylvain Sardy and Donald B. Percival and Andrew
G. Bruce and Hong-Ye Gao and Werner Stuetzle",
journal = SC,
volume = "9",
number = "1",
year = "1999",
pages = "65--75",
URL = "ftp://ftp.statsci.com/pub/WAVELETS/papers/unequal.ps.gz",
keywords = "Nonparametric regression; Wavelet transform;
WaveShrink",
abstract = "Wavelet shrinkage (WaveShrink) is a relatively new
technique for nonparametric function estimation that
has been shown to have asymptotic near-optimality
properties over a wide class of functions. As
originally formulated by Donoho and Johnstone,
WaveShrink assumes equally spaced data. Because so
many statistical applications (e.g., scatterplot
smoothing) naturally involve unequally spaced data,
we investigate in this paper how WaveShrink can be
adapted to handle such data. Focusing on the Haar
wavelet, we propose four approaches that extend the
Haar wavelet transform to the unequally spaced
case. Each approach is formulated in terms of
continuous wavelet basis functions applied to a
piecewise constant interpolation of the observed
data, and each approach leads to wavelet
coefficients that can be computed via a matrix
transform of the original data. For each approach,
we propose a practical way of adapting
WaveShrink. We compare the four approaches in a
Monte Carlo study and find them to be quite
comparable in performance. The computationally
simplest approach (isometric wavelets) has an
appealing justification in terms of a weighted mean
square error criterion and readily generalizes to
wavelets of higher order than the Haar.",
}
@Article{sar:minimax,
title = "Minimax threshold for denoising complex signals with
waveshrink",
author = "Sylvain Sardy",
journal = IEEETSP,
volume = "48",
number = "4",
year = "2000",
pages = "1023--1028",
URL = "http://dmawww.epfl.ch/~sardy/PS/article-minimax.ps",
abstract = "For the problem of signal extraction from noisy
data, Waveshrink has proven to be a powerful tool,
both from an empirical and an asymptotic point of
view. Waveshrink is especially efficient at
estimating spatially inhomogeneous signals, A key
step of the procedure is the selection of the
threshold parameter. Donoho and Johnstone propose a
selection of the threshold based on a minimax
principle, Their derivation is specifically for real
signals and real wavelet transforms. In this paper,
we propose to extend the use of Waveshrink to
denoising complex signals with complex wavelet
transforms. We illustrate the problem of denoising
complex signals with an electronic surveillance
application.",
}
@Unpublished{sar-tse-bru:robust,
title = "Robust Wavelet Denoising",
author = "S. Sardy and P. Tseng and A. G. Bruce",
year = "1998",
note = "Submitted to {\em Journal of the American
Statistical Association}",
URL = "http://dmawww.epfl.ch/~sardy/PS/article-robust.ps",
}
@Article{sca-etal:quasi,
title = "{T}he quasi-periodic oscillations and very low
frequency noise of {S}corpius {X}-1 as transient chaos:
a dripping handrail?",
journal = "Astrophysical Journal Letters",
volume = "411",
number = "2",
year = "1993",
pages = "91--94",
author = "J. D. Scargle and T. {Steiman, Cameron} and K. Young
and D. L. Donoho and J. P. Crutchfield and J. Imamura",
abstract = "The authors present evidence that the quasi-periodic
oscillations (QPO) and very low frequency noise (VLFN)
characteristic of many accretion sources are different
aspects of the same physical process. They analyzed a
long, high time resolution EXOSAT observation of the
low-mass X-ray binary (LMXB) Sco X-1. The X-ray
luminosity varies stochastically on time scales from
milliseconds to hours. The nature of this
variability-as quantified with both power spectrum
analysis and a new wavelet technique, the
scalegram-agrees well with the dripping handrail
accretion model, a simple dynamical system which
exhibits transient chaos. In this method both the QPO
and VLFN are produced by radiation from blobs with a
wide size distribution, resulting from accretion and
subsequent diffusion of hot gas, the density of which
is limited by an unspecified instability to lie below a
threshold.",
keywords = "V818 Sco. 4U 1617-15. variable star. quasi-periodic
oscillations. very low frequency noise. transient
chaos. accretion sources. low-mass X-ray binary. Sco
X-1. X-ray luminosity. power spectrum analysis. wavelet
technique. scalegram. dripping handrail accretion
model. blobs. size distribution. diffusion. hot gas.
density. instability.",
}
@InCollection{sca:astronomical,
title = "Wavelet Methods in Astronomical Time Series Analysis",
author = "Jeffrey D. Scargle",
email = "jeffrey@sunshine.arc.nasa.gov",
pages = "226--248",
crossref = "rao-pri-les:applications",
abstract = "",
}
@InProceedings{sca:astronomical2,
title = "Astronomical Time Series Analysis: {N}ew Methods for
Studying Periodic and Aperiodic Systems",
author = "Jeffrey D. Scargle",
booktitle = "The Weise Observatory 25th Anniversary Symposium:
Astronomical Time Series",
email = "jeffrey@sunshine.arc.nasa.gov",
year = "1996",
abstract = "",
}
@InCollection{sca:detection,
title = "Detection and modeling of chaotic dynamics using
wavelet techniques",
author = "Jeffrey D. Scargle",
email = "jeffrey@sunshine.arc.nasa.gov",
crossref = "szu:wavelet1",
note = "",
URL = "",
abstract = "Powerful new data analysis techniques based on
wavelets are proving extremely useful in the reduction
and interpretation of time series data. The goals of
these methods include denoising, characterizing,
modeling, and compressing of time series data. The
multi-scale nature of wavelet analysis makes it
especially useful for detection and characterization of
self-similar or 'scaling' behavior, such as is common
for chaotic processes. This paper describes how wavelet
techniques led to a transient-chaos model for a rapidly
fluctuating celestial X-ray source. The methods
described here are freely available in a new software
package called TeachWave, developed by David Donoho and
Iain Johnstone of Stanford University (anonymous ftp to
playfair.stanford.edu; the software is in directory
/pub/software/wavelets, and a number of related
technical papers are in /pub/reports).",
}
@InProceedings{sch-swe:sphere,
author = "Peter Schr{\"o}der and Wim Sweldens",
title = "Spherical Wavelets: {E}fficiently Representing
Functions on the Sphere",
booktitle = "Computer Graphics Proceedings (SIGGRAPH 95)",
year = "1995",
publisher = "ACM Siggraph",
pages = "161--172",
URL = "http://cm.bell-labs.com/who/wim/papers/sphere.ps.gz",
abstract = "Wavelets have proven to be powerful bases for use in
numerical analysis and signal processing. Their power
lies in the fact that they only require a small number
of coefficients to represent general functions and
large data sets accurately. This allows compression and
efficient computations. Classical constructions have
been limited to simple domains such as intervals and
rectangles. In this paper we present a wavelet
construction for scalar functions defined on the
sphere. We show how biorthogonal wavelets with custom
properties can be constructed with the lifting scheme.
The bases are extremely easy to implement and allofw
fully adaptive subdivisions. We give examples of
functions defined on the sphere, such as topographic
data, bi-directional reflection distribution functions,
and illumination, and show how they can be efficiently
represented with spherical wavelets.",
}
@Book{sch-web:recent,
title = "Recent Advances in Wavelet Analysis",
booktitle = "Recent Advances in Wavelet Analysis",
editor = "Larry L. Schumaker and Glenn Webb",
volume = "3",
series = "Wavelet Analysis and its Applications",
year = "1993",
publisher = "Academic Press, Inc.",
ISBN = "0-12-632370-4",
abstract = "Recent Advances in Wavelet Analysis is the third
volume in the WAVELET ANALYSIS AND ITS APPLICATIONS
series. This edited volume features ten timely and
important articles authored by various experts in their
respective fields, including such notable contributors
as David L. Donoho, Ingrid Daubechies (MacArthur grant
awardees in ‘91 and ‘92, respectively), Phillippe
Tchamitchian, Patrick Flandrin (both featured speakers
at the ‘92 International Wavelets Conference in
Toulouse), Charles Chui, and Bjorn Jawerth (one of the
editors of the Wavelet Digest). This book covers recent
advances in wavelet analysis and applications in areas
including wavelets on bounded intervals, wavelet
decomposition of special interest to statisticians,
wavelets approach to differential and integral
equations, analysis of subdivision operators, and
wavelets related to problems in engineering and
physics. Anyone interested in the ever-evolving field
of wavelets will find this book an excellent addition
to the series and to the literature overall.",
}
@Article{sch:investigation,
title = "On the investigation of hidden periodicities with
application to a supposed 26-day period of
meterological phenomena",
author = "A. Schuster",
journal = "Terrestrial Magnetism",
volume = "3",
year = "1898",
pages = "13--41",
}
@Article{sch:optimal,
title = "Fast and statistically optimal period search in uneven
sampled observations",
author = "A. Schwarzenberg-Czerny",
journal = ApJ,
volume = "460",
number = "2",
year = "1996",
pages = "107--110",
URL = "http://www.journals.uchicago.edu/ApJ/journal/issues/ApJL/v460n2/5758/5758.html",
abstract = "The classical methods for searching for a periodicity
in uneven sampled observations suffer from a poor match
of the model and true signals and/or use of a statistic
with poor properties. We present a new method employing
periodic orthogonal polynomials to fit the observations
and the analysis of variance (ANOVA) statistic to
evaluate the quality of the fit. The orthogonal
polynomials constitute a flexible and numerically
efficient model of the observations. Among all popular
statistics, ANOVA has optimum detection properties as
the uniformly most powerful test. Our recurrence
algorithm for expansion of the observations into the
orthogonal polynomials is fast and numerically stable.
The expansion is equivalent to an expansion into
Fourier series. Aside from its use of an inefficient
statistic, the Lomb-Scargle power spectrum can be
considered a special case of our method. Tests of our
new method on simulated and real light curves of
nonsinusoidal pulsators demonstrate its excellent
performance. In particular, dramatic improvements are
gained in detection sensitivity and in the damping of
alias periods.",
}
@Article{sch:translation-invariant,
author = "Scholl, D. J.",
title = "Translation-invariant data visualization with
orthogonal discrete wavelets",
journal = IEEETSP,
volume = "46",
number = "7",
year = "1998",
pages = "2031--2034",
abstract = "Orthogonal discrete wavelet transforms, can be made
translation-invariant by adding redundant wavelet
coefficients through repeated shifting operations.
Othogonality is lost, but isometry and compact time
support can be preserved. The practical application to
data visualization of scalograms based on such transforms
is discussed and illustrated with measured transient
signals.",
}
@Article{sel:balanced,
title = "Balanced multiwavelet bases based on symmetric {FIR}
filters",
author = "Selesnick, Ivan W.",
journal = IEEETSP,
volume = "48",
number = "1",
year = "2000",
pages = "184--191",
abstract = "This paper describes a basic difference between
multiwavelets and scalar wavelets that explains,
without using zero moment properties, why certain
complications arise in the implementation of
discrete multiwavelet transforms. Assuming we wish
to avoid the use of prefilters in implementing the
discrete multiwavelet transform, it is suggested
that the behavior of the iterated filter bank
associated with a multiwavelet basis of multiplicity
r is more fully revealed by an expanded set of r(2)
scaling functions phi(i,j). This paper also
introduces new K-balanced orthogonal multiwavelet
bases based on symmetric FIR filters. The nonlinear
design equations arising in this work are solved
using the Grobner basis. The minimal-length
K-balanced multiwavelet bases based on even-length
symmetric FIR filters are better behaved than those
based on odd-length symmetric FIR filters, as
illustrated by special relations they satisfy and by
examples constructed.",
}
@Article{sel:interpolating,
title = "Interpolating multiwavelet bases and the sampling
theorem",
author = "Selesnick, Ivan W.",
journal = IEEETSP,
volume = "47",
number = "6",
year = "1999",
pages = "1615--1621",
email = "seles@taco.poly.edu",
keywords = "filter banks multiwavelet bases sampling wavelet
transforms",
abstract = "This paper considers the classical sampling theorem
in multiresolution spaces with scaling functions as
interpolants. As discussed by Xia and Zhang, for an
orthogonal scaling function to support such a
sampling theorem, the scaling function must be
cardinal (interpolating). They also showed that the
only orthogonal scaling function that is both
cardinal and of compact support is the Haar
function, which is not continuous, This paper
addresses the same question, but in the multiwavelet
context, where the situation is different. This
paper presents the construction of compactly
supported orthogonal multiscaling functions that are
continuously differentiable and cardinal. The
scaling functions thereby support a Shannon-like
sampling theorem, Such wavelet bases are appealing
because the initialization of the discrete wavelet
transform (prefiltering) is the identity operator.",
}
@Article{sel:slantlet,
title = "The Slantlet transform",
author = "Selesnick, Ivan W.",
journal = IEEETSP,
volume = "47",
number = "5",
year = "1999",
pages = "1304--1313",
email = "seles@taco.poly.edu",
keywords = "wavelet transform bases L(2)",
abstract = "The discrete wavelet transform (DWT) is usually
carried out by filterbank iteration; however, for a
fixed number of zero moments, this does not yield a
discrete-time basis that is optimal with respect to
time localization. This paper discusses the
implementation and properties of an orthogonal DWT,
with two zero moments and with improved time
localization. The basis is not based on filterbank
iteration; instead, different filters are used for
each scale. For coarse scales, the support of the
discrete-time basis functions approaches two thirds
that of the corresponding functions obtained by
filterbank iteration, This basis, which is a special
case of a class of bases described by Alpert,
retains the octave-hand characteristic and is
piecewise linear (but discontinuous). Closed-form
expressions for the filters are given, an efficient
implementation of the transform is described, and
improvement in a denoising example is shown. This
basis, being piecewise linear, is reminiscent of the
slant transform, to which it is compared.",
}
@Article{ser-wal-per:properties,
title = "Statistical Properties of the Wavelet Variance
Estimator for Non-{G}aussian/Non-Linear time series",
author = "Abdeslam Serroukh and Andrew T. Walden and Donald B.
Percival",
journal = JASA,
volume = "95",
number = "449",
year = "2000",
pages = "184--196",
URL = "http://www.ma.ic.ac.uk/~atw/Wavar.ps.gz",
}
@Article{ser-wal:bivariate1,
title = "Wavelet scale analysis of bivariate time series {I}:
{M}otivation and estimation",
author = "Abdeslam Serroukh and Andrew T. Walden",
journal = JNS,
volume = "",
number = "",
year = "2000",
pages = "",
note = "to appear",
}
@Article{ser-wal:bivariate2,
title = "Wavelet scale analysis of bivariate time series
{II}: {S}tatistical properties for linear processes",
author = "Abdeslam Serroukh and Andrew T. Walden",
journal = JNS,
volume = "",
number = "",
year = "2000",
pages = "",
note = "to appear",
}
@Article{ses-cso-ste:exponential,
title = "Tests for the Exponential Distribution using
{K}olmogorov-type Statistics",
author = "V. Seshadri and M. Cs{\"o}rg{\H o} and M. A.
Stephens",
journal = JRSSB,
volume = "31",
number = "3",
year = "1969",
pages = "499--509",
}
@Article{sha-hou:on-line,
title = "An on-line wavelet transform for de-noising of high
performance liquid chromatograms",
author = "Xueguang Shao and Shunquan Hou",
journal = "Analytical Letters",
volume = "32",
number = "12",
year = "1999",
pages = "2507--2520",
}
@Article{sha-xia:wavelet,
title = "The Wavelet Analysis Method of Stationary Random
Processes",
author = "Luo Shaoming and Zhang Xiangwei",
journal = "Applied Mathematics and Mechanics",
volume = "19",
number = "10",
year = "1998",
pages = "929--935",
note = "English Edition",
}
@Article{sha-yen:exact,
title = "On the exact values of orthonormal scaling
coefficients of lengths 8 and 10",
author = "Shann, W. C. and Yen, C. C.",
journal = ACHA,
volume = "6",
number = "1",
year = "1999",
pages = "109--112",
abstract = "We show the exact values of the scaling coefficients
of length 8 and 10 for Daubechies' orthonormal
scaling functions.",
}
@Article{she-rob-szu:optical,
title = "Optical Wavelet Transform",
author = "Yunlong Sheng and Donny Roberge and Harold H. Szu",
journal = OE,
volume = "31",
number = "9",
year = "1992",
pages = "1840--1845",
abstract = "The wavelet transform is implemented using an optical
multichannel correlator with a bank of wavelet
transform filters. This approach provides a
shift-invariant wavelet transform with continuous
translation and discrete dilation parameters. The
wavelet transform filters can be in many cases simply
optical transmittance masks. Experimental results show
detection of the frequency transition of the input
signal by the optical wavelet transform.",
}
@Article{she-str:asymptotics,
title = "Asymptotics of {D}aubechies filters, scaling
functions, and wavelets",
author = "Shen, J. H. and Strang, G.",
journal = ACHA,
volume = "5",
number = "3",
year = "1998",
pages = "312--331",
abstract = "We study the asymptotic form as p --> infinity of
the Daubechies orthogonal minimum phase filter h(p)[n],
scaling function phi(p)(t), and wavelet w(p)(t). Kateb
and Lemarie calculated the leading term in the phase of
the frequency response H-p(omega). The infinite product
<(phi)over cap>(p)(omega) = Pi H-p(omega/2(k)) leads us
to a problem in stationary phase, for an oscillatory
integral with parameter t. The leading terms change
form with tau = t/p and we find three regions for
phi(p)(tau): (1) An Airy function up to near tau(0):
root 42 pi/p Ai(-root 42 pi p(2)(tau - tau(0))) +
o(p(-1/3)) (2) An oscillating region root 2/pi
pG'(omega(tau))cos [p(G((-1))(omega(tau)) -
G(omega(tau))omega(tau)) + pi/4] + o(p(-1/2)) (3) A
rapid decay after tau(1): (1/p pi)(1/(tau -
tau(1)))sin[p(G((-1))(pi) - tau pi)] + o(p(-1)) The
numbers tau(0) similar or equal to 0.1817 and tau(1)
similar or equal to 0.3515 are known constants. The
function G and its integral G((-1)) are independent of
p. Regions 1 and 2 are matched over the interval p(-2/3)
much less than tau - tau(0) much less than 1. The
wavelets have a simpler asymptotic expression because
the Airy wavefront is removed by the highpass filter.
We also find the asymptotics of the impulse response
h(p)[n] -a different function g(omega) controls the three
regions. The difficulty throughout is to estimate the
phase.",
}
@Article{she:dwt,
title = "The discrete wavelet transform: {W}edding the \`{a}
trous and {M}allat algorithms",
author = "Mark J. Shensa",
journal = IEEETSP,
volume = "40",
number = "10",
year = "1992",
pages = "2464--2482",
abstract = "Two separately motivated implementations of the
wavelet transform are brought together. It is observed
that these algorithms are both special cases of a
single filter bank structure, the discrete wavelet
transform, the behavior of which is governed by the
choice of filters. In fact, the a trous algorithm is
more properly viewed as a nonorthonormal
multiresolution algorithm for which the discrete
wavelet transform is exact. Moreover, it is shown that
the commonly used Lagrange a trous filters are in
one-to-one correspondence with the convolutional
squares of the Daubechies filters for orthonormal
wavelets of compact support. A systematic framework for
the discrete wavelet transform is provided, and
conditions are derived under which it computes the
continuous wavelet transform exactly. Suitable filter
constraints for finite energy and boundedness of the
discrete transform are also derived. Relevant signal
processing parameters are examined, and it is observed
that orthonormality is balanced by restrictions on
resolution.",
}
@Article{she:inverse,
title = "Discrete inverses for nonorthogonal wavelet
transforms",
author = "M. J. Shensa",
journal = IEEETSP,
volume = "44",
number = "4",
year = "1996",
pages = "798--807",
URL = "ftp://ftp.nosc.mil/pub/Shensa/WTinverse_TR1621.ps.Z",
keywords = "discrete inverses, nonorthogonal wavelet transforms,
signal processing, resolution, standard inversion
procedure, finite expansion, algorithms, Morlet
wavelets",
abstract = "Discrete nonorthogonal wavelet transforms play an
important role in signal processing by offering finer
resolution in time and scale than their orthogonal
counterparts. The standard inversion procedure for such
transforms is a finite expansion in terms of the
analyzing wavelet. While this approximation works quite
well for many signals, it fails to achieve good
accuracy or requires an excessive number of scales for
others. This paper proposes several algorithms that
provide more adequate inversion and compares them in
the case of Morlet wavelets. In the process, both
practical and theoretical issues for the inversion of
nonorthogonal wavelet transforms are discussed.",
}
@Article{shu-fed:shannon,
title = "Analysis and synthesis of $1/f$ processes via Shannon
wavelets",
author = "Shusterman, E. and Feder, M.",
journal = IEEETSP,
volume = "46",
number = "6",
year = "1998",
pages = "1698--1702",
keywords = "nonstationary processes 1/f noise spectral analysis
wavelets",
abstract = "1/f processes can he very useful in modeling processes
with long-term correlation. We propose analysis and
synthesis procedures to express these processes in terms
of the Shannon wavelet. Unlike previous techniques, our
analysis procedure generates uncorrelated decomposition
coefficients for the 1/f process. This is done hy taking
onto account, and then removing, the residual correlation
between the wavelet components. The analysis procedure is
the major contribution of this work. The proposed
synthesis algorithm, which is a byproduct of the proposed
analysis algorithm, is competitive with other
techniques.",
}
@Article{sim-fre-ade-hee:shiftable,
title = "Shiftable multiscale transforms",
author = "Eero P. Simoncelli and William T. Freeman and Edward
H. Adelson and David J. Heeger",
journal = IEEETIT,
volume = "38",
number = "2",
year = "1992",
pages = "587--607",
URL = "ftp://ftp.cis.upenn.edu/pub/eero/simoncelli91.ps.Z",
keywords = "scale domain. orientation domain. signal
analysis. multiscale transforms. orthogonal wavelet
transforms. translation invariance. wavelet
subbands. shiftability. spatial domain. sampling
theorem. shiftable transforms. 1-D
transform. jointly shiftable. scale-space
analysis. stereo disparity measurement. image
enhancement",
abstract = "One of the major drawbacks of orthogonal wavelet
transforms is their lack of translation invariance:
the content of wavelet subbands is unstable under
translations of the input signal. Wavelet transforms
are also unstable with respect to dilations of the
input signal and, in two dimensions, rotations of
the input signal. The authors formalize these
problems by defining a type of translation
invariance called shiftability. In the spatial
domain, shiftability corresponds to a lack of
aliasing; thus, the conditions under which the
property holds are specified by the sampling
theorem. Shiftability may also be applied in the
context of other domains, particularly orientation
and scale. Jointly shiftable transforms that are
simultaneously shiftable in more than one domain are
explored. Two examples of jointly shiftable
transforms are designed and implemented: a 1-D
transform that is jointly shiftable in position and
scale, and a 2-D transform that is jointly shiftable
in position and orientation. The usefulness of these
image representations for scale-space analysis,
stereo disparity measurement, and image enhancement
is demonstrated.",
}
@InProceedings{sim-fre:steerable,
title = "The Steerable Pyramid: {A} Flexible Architecture for
Multi-Scale Derivative Computation",
author = "Eero P. Simoncelli and William T. Freeman",
booktitle = "International Conference on Image Processing",
volume = "3",
address = "23-26 Oct. 1995, Washington, DC, USA",
month = oct,
year = "1995",
pages = "444--447",
URL = "ftp://ftp.cis.upenn.edu/pub/eero/simoncelli95b.ps.Z",
keywords = "flexible architecture multiscale derivative
computation steerable pyramid linear image
decomposition orientation subbands scale subbands
basis functions directional derivative operators
transform filters Fourier domain",
abstract = "We describe an architecture for efficient and
accurate linear decomposition of an image into scale
and orientation subbands. The basis functions of
this decomposition are directional derivative
operators of any desired order. We describe the
construction and implementation of the transform.",
}
@Article{sim-han-nes:determination,
title = "Determination of the Hurst exponent by use of
wavelet transforms",
author = "Simonsen, I. and Hansen, A. and Nes, O. M.",
journal = PRE,
volume = "58",
number = "3",
year = "1998",
pages = "2779--2787",
keywords = "inverse fractal problem surfaces roughness growth",
abstract = "We propose a method for (global) Hurst exponent
determination based on wavelets. Using this method,
we analyze synthetic data with predefined Hurst
exponents, fracture surfaces, and data from
economy. The results are compared to those obtained
with Fourier spectral analysis. When many samples
are available, the wavelet and Fourier methods are
comparable in accuracy. However, when one or only a
few samples are available, the wavelet method
outperforms the Fourier method by a large margin.",
}
@TechReport{sli-etal:intraseasonal,
title = "Intraseasonal oscillations in 15 atmospheric general
circulation models (results from an {AMIP} diagnostic
subproject)",
author = "J. M. Slingo and K. R. Sperber and J. S. Boyle and
J.-P. Ceron and M. Dix and B. Dugas and W. Ebisuzaki
and J. Fyfe and D. Gregory and J.-F. Gueremy and J.
Hack and A. Harzallah and P. Inness and A. Kitoh and W.
K.-M. Lau and B. McAvaney and R. Madden and A. Matthews
and T. N. Palmer and C.-K. Park and D. Randell and N.
Renno",
number = "661",
institution = "World Meteorological Organization",
year = "1995",
}
@Article{son-wu:multiscale,
title = "Multiscale interrelations between air temperature in
southeast {C}hina and {E}l {N}ino: {W}avelet
analysis",
author = "Sonechkin, D. M. and Wu, H. B.",
journal = "Izvestiya Akademii Nauk Fizika Atmosfery I Okeana",
volume = "35",
number = "2",
year = "1999",
pages = "250--258",
keywords = "seasonal cycle oscillation transform chaos",
abstract = "Multiscale manifestations of the El Nino-Southern
Oscillation in the dynamics of air temperature in
various regions of the earth were examined, using
southeast China as an example. The wavelet
transforms of surface air temperature time series
observed in Guangzhou (southeast China) and sea
surface temperature time series observed in the Nine
1 + 2 and Nino 3 regions were analyzed. An intense
interdecadal oscillation was revealed in these time
series. The subsequent correlation of the
transformed series separately for each time scale,
which is a new technique designed to analyze
interrelations of nonstationary stochastic
processes, showed that the interrelations between
these series are complex in character. This
manifests itself in positive and negative
correlations between the series on interannual and
interdecadal scales, respectively. Since the
interdecadal variability is determined. by a
sequence of extremely intense El Nino events, it
follows that the response of the Guangzhou
temperature to intense El Nino is other than that to
routine El Nino.",
note = "In Russian",
}
@Article{spo:adaptive,
title = "Adaptive hypothesis testing using wavelets",
author = "V. G. Spokoiny",
journal = AofS,
volume = "24",
number = "6",
year = "1996",
pages = "??--??",
abstract = "",
}
@Article{sta-zee:filter-banks,
title = "Two-dimensional orthogonal filter banks and wavelets
with linear phase",
author = "Stanhill, D. and Zeevi, Y. Y.",
journal = IEEETSP,
volume = "46",
number = "1",
year = "1998",
pages = "183--190",
keywords = "filter banks linear phase symmetry 2-D wavelets",
URL = "ftp://ftp.technion.ac.il/pub/supported/ee/Signal_processing/2dlp.ps.gz",
abstract = "Two-dimensional (2-D) compactly supported,
orthogonal wavelets and filter banks having linear
phase are presented, Two cases are discussed:
wavelets with two-fold symmetry (centrosymmetric)
and wavelets with four-fold symmetry that are
symmetric (or anti-symmetric) about the vertical and
horizontal axes. We show that imposing the
requirement of linear phase in the case of
order-factorable wavelets imposes a simple
constraint on each of its polynomial order-1
factors, We thus obtain a simple and complete method
of constructing orthogonal order-factorable wavelets
with linear phase, This method is exemplified by
design in the case of four-band separable
sampling. An interesting result that is similar to
the one well-known in the one-dimensional (1-D) case
is obtained: Orthogonal order-factorable wavelets
cannot be both continuous and have four-fold
symmetry.",
}
@Article{sta-zee:wavelets,
title = "Two-dimensional orthogonal wavelets with vanishing
moments",
author = "Stanhill, D. and Zeevi, Y. Y.",
journal = IEEETSP,
volume = "44",
number = "10",
year = "1996",
pages = "2579--2590",
keywords = "reconstruction filter banks regularity matrices
design",
URL = "ftp://ftp.technion.ac.il/pub/supported/ee/Signal_processing/2dvm.ps.gz",
abstract = "We investigate a very general subset of 2-D,
orthogonal, compactly supported wavelets, This
subset includes all the wavelets with a
corresponding wavelet (polyphase) matrix that can be
factored as a product of factors of degree-1 in one
variable. In this paper, we consider, in particular,
wavelets with vanishing moments, The number of
vanishing moments that can be achieved increases
with the increase in the McMillan degrees of the
wavelet matrix. We design wavelets with the maximal
number of vanishing moments for given McMillan
degrees by solving a set of nonlinear constraints on
the free parameters defining the wavelet matrix and
discuss their relation to regular, smooth wavelets,
Design examples are given for two fundamental
sampling schemes: the quincunx and the four-band
separable sampling, The relation of the wavelets to
the well-known 1-D Daubechies wavelets with
vanishing moments is discussed.",
}
@InProceedings{sta-mur-bij:multi,
title = "Multiresolution and Astronomical Image Processing",
author = "J. L. Stark and F. Murtagh and A. Bijaoui",
booktitle = "Astronomical Data Analysis Software and Systems IV",
editor = "R. A. Shaw and H. E. Payne and J. J. E. Hayes",
series = "ASP Conference Series",
volume = "77",
year = "1995",
pages = "279--288",
URL = "http://http.hq.eso.org/~fmurtagh/adass-jls.ps",
abstract = "We present several wavelet transform algorithms and
their applications in astronomical image processing
(restoration, object detection, compression, etc.).",
}
@Article{sta-sie-gre:spectral,
title = "Spectral analysis using the wavelet transform",
author = "Starck J. L. and Siebenmorgen R. and Gredel R.",
journal = ApJ,
volume = "482",
number = "2",
pages = "1011--1020",
year = "1997",
URL = "http://www.journals.uchicago.edu/ApJ/cgi-bin/resolve?1997ApJ...482.1011SMPS",
keywords = "infrared, stars. methods, observational. stars,
individual (HH 100). stars, pre-main-sequence.
techniques, spectroscopic.",
abstract = "We introduce a new signal processing technique to
analyze noisy spectra. The method is based on the
wavelet transform and employs the a trous algorithm.
Noise determination and detection criteria are
discussed in detail, together with pitfalls related to
the use of wavelets in the analysis of spectra.
Simulations are presented to demonstrate the power and
the shortcomings of our method. We apply our technique
to the case of continuum sources that show superposed
interstellar or circumstellar absorption or emission
bands that are shallow and broad. In particular, we
analyze an L-band spectrum of the Herbig-Haro energy
source HH 100 IRS. The analysis indicates the presence
of a shallow emission band near 3.51 mu m that is
tentatively assigned to arise from aliphatic (CH2)
vibrations.",
}
@Article{ste-pav-boj:nao,
title = "Is the {N}orth {A}tlantic {O}scillation a random
walk?",
author = "Stephenson, D. B. and Pavan, V. and Bojariu, R.",
journal = IJC,
volume = "20",
number = "1",
year = "2000",
pages = "1--18",
abstract = "The North Atlantic Oscillation (NAO) is a major mode
of large-scale climate variability which contains a
broad spectrum of variations. There are substantial
contributions from short-term 2-5 year variations,
which have clearly marked teleconnections. Decadal
trends are also apparent in the historical record of
the NAO and may be due to either stochastic or
deterministic processes. Evidence is presented that
suggests the NAO exhibits 'long-range' dependence
having winter values residually correlated over many
years. Several simple stochastic models have been
used to fit the NAO SLP (sea-level pressure)
wintertime index over the period 1864-1998, and
their performance at predicting the following year
has been assessed. Long-range fractionally
integrated noise provides a better fit than does
either stationary red noise or a non-stationary
random walk.",
}
@Article{ste:edf,
title = "{EDF} Statistics for Goodness of Fit and Some
Comparisons",
author = "M. A. Stephens",
journal = JASA,
volume = "69",
number = "347",
pages = "730--737",
year = "1974",
keywords = "Normal distribution; Exponential distribution; Power;
Anderson-Darling statistic; Cram{\'e}r-von Mises test;
Kolmogorov-Smirnov test; EDF = empirical distribution
function",
}
@Article{ste:estimation,
title = "Estimation of the mean of a multivariate normal
distribution",
author = "Charles M. Stein",
journal = AofS,
volume = "9",
number = "6",
year = "1981",
pages = "1135--1151",
}
@InCollection{ste:tests-edf,
title = "Tests Based on {EDF} Statistics",
author = "Michael A. Stephens",
pages = "97--193",
crossref = "dag-ste:goodness",
note = "",
URL = "",
abstract = "",
}
@InCollection{ste:tests-exp,
title = "Tests for the Exponential Distribution",
author = "Michael A. Stephens",
pages = "421--459",
crossref = "dag-ste:goodness",
note = "",
URL = "",
abstract = "",
}
@Article{ste:use,
title = "Use of the {K}olmogorov--{S}mirnov, {C}ram{\'e}r--von
{M}ises and related statistics without extensive
tables",
author = "Michael A. Stephens",
journal = JRSSB,
volume = "32",
number = "1",
year = "1970",
pages = "115--122",
}
@Article{sto-lan-ngy:practical,
title = "Practical synthesis of accurate fractal images",
author = "M. A. Stosik and R. G. Lane and D. T. Nguyen",
journal = "Graphical Models and Image Processing",
volume = "57",
number = "3",
year = "1995",
pages = "206--219",
abstract = "This paper compares the synthesis of fractal images
using both wavelets and a modified form of the
random midpoint displacement algorithm. The accuracy
of the generated fractal is investigated by an
analysis of its second-order temporal statistics. It
is shown that, although wavelets can be used to
produce a good approximation to fractional Brownian
motion, a technique based on the random midpoint
displacement algorithm is in practice much simpler
to implement, faster to generate, and results in a
comparable accuracy. Furthermore the proposed method
is shown to be considerably more efficient
computationally.",
}
@Unpublished{sto:remarks,
title = "Remarks on the Unsubsampled Wavelet Transform and the
Lifting Scheme",
author = "Alexander Stoffel",
year = "1998",
note = "Submitted to {\em Signal Processing}",
}
@Unpublished{str-etal:multiwavelet,
title = "The Application of Multiwavelet Filter Banks to Image
Processing",
author = "V. Strela and P. N. Heller and G. Strang and P.
Topiwala and C. Heil",
year = "1995",
note = "Submitted to {\em IEEE Transactions on Image
Processing}",
URL = "http://www-math.mit.edu/~gs/papers/mw_journal.ps.gz",
}
@Article{str-hah:mammograms,
title = "Wavelet Transforms for Detecting Microcalcifications
in Mammograms",
author = "Robin N. Strickland and Hee Il Hahn",
journal = IEEETMI,
volume = "15",
number = "2",
year = "1996",
pages = "218--229",
email = "strickland@ece.arizona.edu",
abstract = "Clusters of fine, granular microcalcifications in
mammograms may be an early sign of disease. Individual
grains are difficult to detect and segment due to size
and shape variability and because the background
mammogram texture is typically inhomogeneous. We
develop a two-stage method based on wavelet transforms
for detecting and segmenting calcifications. The first
stage is based on an undecimated wavelet transform,
which is simply the conventional filter bank
implementation without downsampling, so that the
low-low (LL), low-high (LH), high-low (HL), and
high-high (HH) sub-bands remain at full size. Detection
takes place in HH and the combination LH+HL. Four
octaves are computed with two inter- octave voices for
finer scale resolution. By appropriate selection of the
wavelet basis the detection of microcalcifications in
the relevant size range can be nearly optimized. In
fact, the filters which transform the input image into
HH and LH+HL are closely related to prewhitening
matched filters for detecting Gaussian objects
(idealized microcalcifications) in two common forms of
Markov (background) noise. The second stage is designed
to overcome the limitations of the simplistic Gaussian
assumption and provides an accurate segmentation of
calcification boundaries. Detected pixel sites in HH
and LH+HL are dilated then weighted before computing
the inverse wavelet transform. Individual
microcalcifications are greatly enhanced in the output
image, to the point where straightforward thresholding
can be applied to segment them. FROC curves are
computed from tests using a freely distributed database
of digitized mammograms.",
}
@Book{str-ngu:book,
author = "Gilbert Strang and Truong Nguyen",
title = "Wavelets and Filter Banks",
publisher = "Wellesley-Cambridge Press",
year = "1996",
address = "Wellesley, MA",
URL = "http://saigon.ece.wisc.edu/~waveweb/Tutorials/overview.html",
abstract = "This new textbook by Gilbert Strang and Truong Nguyen
offers a clear and easy-to-understand introduction to
two central ideas -- filter banks for discrete signals,
and wavelets. The connections are fully explained --
the wavelet is determined by a choice of filter
coefficients. All important wavelet properties
(orthogonality or biorthogonality, symmetry, accuracy
of approximation, and smoothness) come from specific
properties of the filters. The text shows how to
construct those filters and wavelets. The applications
are very widespread -- and they continue to develop
rapidly. The book gives a direct approach to signal
processing and image processing through filter banks
that iterate on the lowpass filter (this is the wavelet
idea). Blocking and ringing artifacts are analyzed,
along with many MATLAB applications. Wavelets and
Filter Banks is written for the very broad audience
that uses these ideas: Digital Signal Processing and
Speech Processing, Image Processing including Medical
Imaging, Scientific and Engineering Applications,
Students and Professionals (wanting to understand
wavelets!)",
}
@InCollection{str-sie:haar,
title = "The {H}aar Wavelet Transform in the Time Series
Similarity Paradigm",
author = "Z. R. Struzik and A. P. J. M. Siebes",
booktitle = "Principles of Data Mining and Knowledge Discovery",
editor = "J. M. Zytkow and J. Rauch",
publisher = "Springer-Verlag",
address = "Berlin",
pages = "12--22",
year = "1999",
email = "Zbigniew.Struzik@cwi.nl",
abstract = "Similarity measures play an important role in many
data mining algorithms. To allow the use of such
algorithms on non-standard databases, such as
databases of financial time series, their similarity
measure has to be defined. We present a simple and
powerful technique which allows for the rapid
evaluation of similarity between time series in
large data bases. It is based on the orthonormal
decomposition of the time series into the Haar
basis. We demonstrate that this approach is capable
of providing estimates of the local slope of the
time series in the sequence of multi-resolution
steps. The Haar representation and a number of
related represenations derived from it are suitable
for direct comparison, e.g. evaluation of the
correlation product. We demonstrate that the
distance between such representations closely
corresponds to the subjective feeling of similarity
between the time series. In order to test the
validity of subjective criteria, we test the records
of currency exchanges, finding convincing levels of
correlation.",
}
@InProceedings{str-sie:iwoss99,
title = "Measuring Time Series' Similarity through Large
Singular Features Revealed with Wavelet
Transformation",
author = "Z. R. Struzik and A. P. J. M. Siebes",
booktitle = "Proceedings of the International Workshop on
Database and Expert Systems Application",
month = "September",
publisher = "IEEE Computer Society Press",
address = "Florence, Italy",
year = "1999",
pages = "162--166",
abstract = "For the majority of data mining applications, there
are no models of data which would facilitate the
task of comparing records of time series. We propose
a generic approach to comparing noise time series
using the largest deviations from consistent
statistical behaviour. For this purpose we use a
powerful framework based on wavelet decomposition,
which allows filtering polynomial bias, while
capturing the essential singular behaviour. In
addition, we are able to reveal scale-wise ranking
of singular events including their scale free
characteristic: the Hoelder exponent.",
}
@InProceedings{str-sie:pakdd98,
title = "Wavelet Transform in Similarity Paradigm",
author = "Z. R. Struzik and A. P. J. M. Siebes",
booktitle = "Proceedings of the Pacific-Asia Conference on
Knowledge Discovery and Data Mining",
series = "Lecture Notes in Artificial Intelligence",
volume = "1394",
month = "April",
pages = "295--309",
year = "1998",
address = "Melbourne, Australia",
abstract = "Searching for similarity in time series finds still
broader applications in data mining. However, due to
the very broad spectrum of data involved, there is
no possibility of defining one single notion of
similarity suitable to serve all applications. We
present a powerful framework based on wavelet
decomposition, which allows designing and
implementing a variety of criteria for the
evaluation of similarity between time series. As an
example, two main classes of similarity measures are
considered. One is the global, statistical
similarity, which uses the wavelet transform derived
Hurst exponent to classify time series according to
their global scaling properties. The second measure
estimates similarity locally using the
scale-position bifurcation representation.",
}
@TechReport{str-sie:paradigm1,
title = "Wavelet transform in similarity paradigm {I}",
author = "Zbigniew R. Struzik and Arno P. J. M. Siebes",
number = "INS-R9802",
institution = "CWI, Amsterdam, The Netherlands",
year = "1998",
abstract = "Searching for similarity in time series finds still
broader applications in data mining. However, due to
the very broad spectrum of data involved, there is
no possibility of defining one single notion of
similarity suitable to serve all applications.",
}
@TechReport{str-sie:paradigm2,
title = "Wavelet transform in similarity paradigm {II}",
author = "Zbigniew R. Struzik and Arno P. J. M. Siebes",
number = "INS-R9815",
institution = "CWI, Amsterdam, The Netherlands",
year = "1998",
abstract = "For the majority of data mining applications, there
are no models of data which would facilitate the
tasks of comparing records of time series, thus
leaving one with `noise' as the only description. We
propose a generic approach to comparing noise time
series using the largest deviations from consistent
statistical behaviour. For this purpose we use a
powerful framework based on wavelet decomposition,
which allows filtering polynomial bias, while
capturing the essential singular behaviour. In
particular we are able to reveal scale-wise ranking
of singular events including their scale-free
characteristic: the H{\"o}lder exponent. We use such
characteristics to design a compact representation
of the time series suitable for direct comparison,
e.g. evaluation of the correlation product. We
demonstrate that the distance between such
representations closely corresponds to the
subjective feeling of similarity between the time
series. In order to test the validity of subjective
criteria, we test the records of currency exchanges,
finding convincing levels of (local) correlation.",
}
@Article{str-str:multiwavelets,
title = "Orthogonal multiwavelets with vanishing moments",
author = "Gilbert Strang and Vasily Strela",
journal = OE,
volume = "33",
number = "7",
year = "1994",
pages = "2104--2107",
email = "gs@math.mit.edu",
URL = "",
keywords = "vanishing moments dilation equation scaling function
low-pass filter high-pass filter matrices vectors
translation finite energy matrix coefficients piecewise
linear orthogonal wavelets orthogonal multiwavelets",
abstract = "A scaling function is the solution to a dilation
equation Phi(t)= Sigma c/sub k/ Phi (2t-k), in which
the coefficients come from a low-pass filter. The
coefficients in the wavelet W(t)= Sigma d/sub k/ Phi
(2t-k) come from a high-pass filter. When these
coefficients are matrices, Phi and W are vectors: there
are two or more scaling functions and an equal number
of wavelets. By dilation and translation of the
wavelets, we have an orthogonal basis W/sub ijk/=W/sub
i/(2/sup j/t-k) for all functions of finite energy.
These ``multiwavelets'' open new possibilities. They
can be shorter, with more vanishing moments, than
single wavelets. They can be symmetric, which is
impossible for scalar wavelets (except for Haar's). We
determine the conditions to impose on the matrix
coefficients c/sub k/ in the design of multiwavelets,
and we construct a new pair of piecewise linear
orthogonal wavelets with two vanishing moments.",
}
@TechReport{str-wal:denoising,
title = "Signal and Image denoising via wavelet thresholding:
{O}rthogonal and biorthogonal, scalar and multiple
wavelet transforms",
author = "Vasily Strela and Andrew T. Walden",
number = "TR-98-01",
institution = "Statistics Section, Department of Mathematics,
Imperial College of Science, Technology \& Medicine",
year = "1998",
}
@InProceedings{str-wal:orthogonal,
title = "Orthogonal and biorthogonal multiwavelets for signal
denoising and image compression",
author = "Vasily Strela and Andrew T. Walden",
crossref = "szu:wavelet5",
}
@Article{str:brief,
title = "Wavelets and Dilation Equations: {A} Brief
Introduction",
author = "Gilbert Strang",
journal = SIREV,
volume = "31",
number = "4",
year = "1989",
pages = "614--627",
URL = "http://www-math.mit.edu/~gs/papers/siamrev.ps.gz",
abstract = "This is an introduction to the construction of
wavelets from the solution to a dilation equation. It
discusses the approximation and orthogonal properties
of wavelets and describes the recursive algorithms that
decompose and reconstruct a function. The object of
wavelets is to localize as far as possible in both time
and frequency, with efficient algorithms.",
}
@Unpublished{str:creating,
title = "Creating and Comparing Wavelets",
author = "Gilbert Strang",
year = "1996",
note = "Department of Mathematics, Massachusetts Institute of
Technology",
URL = "http://www-math.mit.edu/~gs/papers/dundee.ps.gz",
email = "gs@math.mit.edu",
}
@InCollection{str:ftae99,
title = "Local Effective H{\"o}der Exponent Estimation on the
Wavelet Transform Maxima Tree",
author = "Z. R. Struzik",
booktitle = "Fractals: Theory and Applications in Engineering",
editor = "Michel Dekking and Jacques L\'{e}vy V\'{e}hel and
Evelyne Lutton and Claude Tricot",
address = NY,
publisher = "Springer-Verlag",
pages = "93--112",
year = "1999",
abstract = "We present a robust method of estimating an
effective Holder exponent locally at an arbitrary
resolution. The method is motivated by the
multiplicative cascade paradigm, and implemented on
the hierarchy of singularities revealed with the
wavelet transform modulus maxima tree. In addition,
we illustrate the possibility of the direct
estimation of the scaling spectrum of the effective
Holder exponent, and we link it to the established
partition functions based multifractal formalism. We
motivate both the local and the global multifractal
analysis by showing examples of computer generated
and real life time series.",
}
@Article{str:make,
title = "How to Make Wavelets",
author = "Robert S. Strichartz",
journal = AMM,
volume = "100",
number = "6",
year = "1993",
pages = "539--557",
keywords = "Fourier analysis, Matrices, Norms, Matrix mechanics",
abstract = "Wavelet bases where Haar functions are constructed
from a single function by dyadic dilations and integer
translations are considered as approximate definitions
of a wavelet expansion. First, a scaling function and
associated multiresolution analysis are chosen. The
orthonormality conditions should be satisfied by
generation of a multiresolution analysis of the
function. The wavelets are then constructed by solving
two algebraic identities and establishing the
properties of the wavelet functions.",
}
@PhdThesis{str:thesis,
title = "Multiwavelets: Theory and Applications",
author = "Vasily Strela",
school = "Massachusetts Institute of Technology",
year = "1996",
URL = "http://pascal.dartmouth.edu/~strela/vvthmain.ps",
}
@Article{str:versus,
title = "Wavelet transforms versus {F}ourier transforms",
author = "Gilbert Strang",
journal = BAMathS,
volume = "28",
number = "2",
year = "1993",
pages = "288--305",
abstract = "An orthogonal basis for piecewise constant functions
is constructed by dilation and translation. The
wavelength transform maps each function to its
coefficients with respect to this basis. The
approximation is found to be poor and is improved by
dilation equations. Higher-order wavelets are
constructed and indirect and recursive methods are used
to compute them. The practicality of the wavelet
transform and Fourier transform in signal processing
are discussed.",
}
@Article{str:wavelets,
title = "Wavelets",
author = "G. Strang",
journal = "American Scientist",
volume = "82",
year = "1994",
pages = "250--255",
URL = "http://www-math.mit.edu/~gs/papers/amsci.ps.gz",
abstract = "The transformation of signals into a sum of small,
overlapping waves offers a new method for analyzing,
storing and transmitting information. The author
discusses: Fourier and wavelet transforms; choosing the
best basis; higher dimensions; fast wavelet transform;
Daubechies wavelets; high-definition television; the
future of fingerprints.",
}
@Unpublished{swe-sch:building,
title = "Building Your Own Wavelets at Home",
author = "Wim Sweldens and Peter Schr{\"o}der",
year = "1996",
note = "In ``Wavelets in Computer Graphics'', ACM SIGGRAPH
Course Notes",
URL = "http://cm.bell-labs.com/who/wim/papers/athome.ps.gz",
abstract = "We give an practical overview of three simple
techniques to construct wavelets under general
circumstances: interpolating subdivision, average
interpolation, and lifting. We include examples
concerning the construction of wavelets on an interval,
weighted wavelets, and wavelets adapted to irregular
samples.",
}
@Article{swe:future,
author = "W. Sweldens",
title = "Wavelets: {W}hat Next?",
journal = "Proc. IEEE",
volume = "84",
number = "4",
pages = "680--685",
year = "1996",
URL = "http://cm.bell-labs.com/who/wim/papers/future.ps",
abstract = "In this concluding article, we want to look ahead and
see what the future can bring to wavelet research. We
try to find a common denominator for ``wavelets'' and
identify promising research directions and challenging
problems.",
}
@Article{swe:lift1,
author = "W. Sweldens",
title = "The lifting scheme: {A} custom-design construction of
biorthogonal wavelets",
journal = "Appl. Comput. Harmon. Anal.",
volume = "3",
number = "2",
pages = "186--200",
year = "1996",
URL = "http://cm.bell-labs.com/who/wim/papers/lift1.ps",
abstract = "We present the lifting scheme, a new idea of
constructing compactly supported wavelets with
compactly supported duals. The lifting scheme provides
a simple relationship between all multiresolution
analyses with the same scaling function. It isolates
the degrees of freedom remaining after fixing the
biorthogonality relations. Then one has full control
over these degrees of freedom to custom-design the
wavelet for a particular application. It also leads to
a faster implementation of the fast wavelet transform.
We illustrate the use of the lifting scheme in the
construction of wavelets with interpolating scaling
functions.",
}
@TechReport{swe:lift2,
author = "W. Sweldens",
title = "The lifting scheme: {A} construction of second
generation wavelets",
institution = "Department of Mathematics, University of South
Carolina",
number = "1995:6",
year = "1995",
URL = "http://cm.bell-labs.com/who/wim/papers/lift2.ps",
abstract = "We present the lifting scheme, a simple construction
of second generation wavelets, wavelets that are not
necessarily translates and dilates of one fixed
function. Such wavelets can be adapted to intervals,
domains, surfaces, weights, and irregular samples. We
show how the lifting scheme leads to a faster, in-place
calculation of the wavelet transform. Several examples
are included.",
}
@InProceedings{swe:spie95,
author = "W. Sweldens",
title = "The Lifting Scheme: {A} New Philosophy in Biorthogonal
Wavelet Constructions",
pages = "68--79",
crossref = "lai-uns:wavelet3",
URL = "http://cm.bell-labs.com/who/wim/papers/spie95.ps",
abstract = "In this paper we present the basic idea behind the
lifting scheme, a new construction of biorthogonal
wavelets which does not use the Fourier transform. In
contrast with earlier papers we introduce lifting
purely from a wavelet transform point of view and only
consider the wavelet basis functions in a later stage.
We show how lifting leads to a faster, fully in-place
implementation of the wavelet transform. Moreover, it
can be used in the construction of second generation
wavelets, wavelets that are not necessarily translates
and dilates of one function. A typical example of the
latter are wavelets on the sphere.",
}
@Article{sza-gal-kis:application2,
title = "{A}pplication of wavelet analysis in variable star
research. {II}. {T}he semiregular star {V} {B}ootis",
journal = AandA,
volume = "308",
number = "3",
year = "1996",
pages = "791--8",
author = "K. Szatmary and J. Gal and L. L. Kiss",
abstract = "For pt.I see Astron. Astrophys. Suppl. Ser., vol.108,
no.2, p.377-94 (1994). Light curve analysis of the
SRa-type variable V Boo is presented and discussed. The
periods are determined and the stability of these
periods as well as their amplitudes are investigated
with wavelet analysis. The amplitude decrease is
studied with the so-called ridge procedure, which shows
that the amplitude of the longer period strongly
decreased while the amplitude of the shorter period
seems to remain stable. The possible interpretations of
this effect are discussed. Using theoretical models and
observational relations physical parameters and
pulsational modes of V Boo are also estimated.",
keywords = "wavelet analysis, variable star research, light curve
analysis, sra type variable, periods, period stability,
period amplitudes, amplitude decrease, ridge procedure,
interpretations, theoretical models, observational
relations, physical parameters, pulsational modes.",
}
@Article{sza-vin-gal:application1,
title = "{A}pplication of wavelet analysis in variable star
research. {I}. {P}roperties of the wavelet map of
simulated variable star light curves",
journal = "AASS",
volume = "108",
number = "2",
year = "1994",
pages = "377--394",
author = "K. Szatmary and J. Vinko and J. Gal",
email = "K.Szatmary@physx.u-szeged.hu,
vinko@physx.u-szeged.hu",
abstract = "A type of the relatively new time-frequency method,
the wavelet analysis is studied. Some results of
testing this method are presented. The test data series
were defined so that they show similarities with the
light variations of variable stars. The effects of
observational noise and irregularities in data sampling
are pointed out. The wavelet analysis seems to be a
suitable method for detecting the local behaviour of
the light curves, e.g. phase jump or mode switching.
The investigation of time-dependent phenomena, e.g.
amplitude or frequency modulation, is more available
than in the case of standard Fourier analysis. In order
to interpret the real wavelet maps of variable stars it
is necessary to take into account the properties of the
method presented by similar tests.",
keywords = "stellar photometry, measurement technique, variable
star light curve, wavelet analysis, variable star,
wavelet map, light curve, time-frequency method,
observational noise, irregularities, method.",
}
@Article{szi-kat-par-alb-cah:local,
title = "The local effect of intermittency on the inertial
subrange energy spectrum of the atmospheric surface
layer",
author = "Jozsef Szilagyi and Gabriel G. Katul and Marc B.
Parlange and John D. Albertson and Anthony T. Cahill",
journal = BLM,
volume = "79",
number = "1--2",
year = "1996",
pages = "35--50",
abstract = "Orthonormal wavelet expansions are applied to
atmospheric surface layer velocity measurements. The
effect of intermittent events on the energy spectrum of
the inertial subrange is investigated through analysis
of wavelet coefficients. The local nature of the
orthonormal wavelet transform in physical space makes
it possible to identify a relationship between the
inertial subrange slope of the local wavelet spectrum
and a simple indicator (i.e. the local variance of the
signal) of local intermittency buildup. The slope of
the local wavelet energy spectrum in the inertial
subrange is shown to be sensitive to the presence of
intermittent events. During well-developed intermittent
events (coherent structures), the slope of the energy
spectrum is somewhat steeper than -5/3, while in less
active regions the slope is found to be flatter than
-5/3. When the slopes of local wavelet spectra are
ensemble averaged, a slope of -5/3 is recovered for the
inertial subrange.",
}
@Article{tac:differentiation,
title = "The differentiation by a wavelet and its application
to the estimation of a transfer function",
author = "Tachibana, Y.",
journal = IEICETFECCS,
volume = "E81A",
number = "6",
year = "1998",
pages = "1194--1200",
keywords = "wavelet digital filter differential filters digital
signal processing identification parameters estimation
step response",
abstract = "This paper deals with a set of differential operators
for calculating the differentials of an observed signal
by the Daubechies wavelet and its application for the
estimation of the transfer function of a linear system
by using non-stationary step-like signals. The
differential operators are constructed by iterative
projections of the differential of the scaling function
for a multiresolution analysis into a dilation subspace.
By the proposed differential operators we can extract the
arbitrary order differentials of a signal. We propose a
set of identifiable filters constructed by the sum of
multiple filters with the first order lag
characteristics. Using the above differentials and the
identifiable filters we propose an identification method
for the transfer function of a linear system. In order
to ensure the appropriateness and effectiveness of the
proposed method some numerical simulations are
presented.",
}
@InProceedings{tas:near-best,
title = "Near-best basis selection algorithms with
non-additive information cost functions",
author = "Taswell, C.",
booktitle = "Proceedings of the IEEE-SP International Symposium
on Time- Frequency and Time-Scale Analysis",
editor = "M. G. Amin",
publisher = "IEEE Press",
address = "Philadelphia, PA",
year = "1994",
pages = "13--16",
URL = "http://www.wavebox.com/NBBSA94.ps",
keywords = "near-best basis selection algorithms non-additive
information cost functions search algorithms signal
decomposition decision criteria wavelet packet
transforms additive information costs matching
pursuit decomposition time- frequency analysis data
compression",
abstract = "Search algorithms for finding signal decompositions
called near-best bases using decision criteria
called non-additive information costs are proposed
for selecting bases in wavelet packet
transforms. These new methods are compared with the
best bases and additive information costs of Coifman
and Wickerhauser (see IEEE Trans. Information
Theory, vol.38, p.713-18, 1992). All near-best and
best bases were also compared with the matching
pursuit decomposition of Mallat and Zhang (see IEEE
Trans. Signal Processing, vol.41, p.3397-3415,
1993). Preliminary experiments suggest that for the
application of time-frequency analysis, a wide
variety of results can be obtained with the
different methods, and that for the application of
data compression, the near-best basis selected with
non-additive costs may outperform the best basis
selected with additive costs.",
}
@Article{tas:satisficing,
title = "Satisficing search algorithms for selecting
near-best bases in adaptive tree-structured wavelet
transforms",
author = "Taswell, C.",
journal = IEEETSP,
volume = "44",
number = "10",
year = "1996",
pages = "2423--2438",
URL = "http://www.wavebox.com/SSANBB96.ps",
keywords = "image compression speech",
abstract = "Satisficing search algorithms are proposed for
adaptively selecting near-best basis and near-best
frame decompositions in redundant tree-structured
wavelet transforms, Any of a variety of additive or
nonadditive information cost functions can be used
as the decision criterion for comparing and
selecting nodes when searching through the tree,The
algorithms are applicable to tree-structured
transforms generated by any kind of wavelet whether
orthogonal, biorthogonal, or nonorthogonal, These
satisficing search algorithms implement
suboptimizing rather than optimizing principles, and
acquire the important advantage of reduced
computational complexity with significant savings in
memory, flops, and time, Despite the suboptimal
approach, top-down tree-search algorithms with
additive or nonadditive costs that yield near-best
bases can be considered, in certain important and
practical situations, better than bottom-up
tree-search algorithms with additive costs that
yield best bases, Here, ''better than'' means that,
effectively, the same level of performance can be
attained for a relative fraction of the
computational work, Experimental results comparing
the various information cost functions and basis
selection methods are demonstrated for both data
compression of real speech and time- frequency
analysis of artificial transients.",
}
@InCollection{tas:top-down,
title = "Top-Down and Bottom-Up Tree Search Algorithms for
Selecting Bases in Wavelet Packet Transforms",
author = "Carl Taswell",
crossref = "ant-opp:wavelets",
pages = "???--???",
URL = "http://www.wavebox.com/TDBUTSA94.ps",
keywords = "",
abstract = "Search algorithms for finding signal decompositions
called near-best bases using decision criteria
called non-additive information costs have recently
been proposed by Taswell for selecting bases in
wavelet packet transforms represented as binary
trees. These methods are extended here to
distinguish between top-down and bottom-up tree
searches. Other new non-additive information cost
functions are also proposed. In particular, the
near-best basis with the non-additive cost of the
Shannon entropy on probabilities is compared against
the best basis with the additive cost of the
Coifman-Wickerhauser entropy on energies. All
wavelet packet basis decompositions are also
compared with the nonorthogonal matching pursuit
decomposition of Mallat and Zhang and the orthogonal
matching pursuit decomposition of Pati et al. Monte
Carlo experiments using a constant-bit-rate
variable-distortion paradigm for lossy compression
suggest that the statistical performance of top-down
near-best bases with non-additive costs is superior
to that of bottom-up best bases with additive
costs. Top-down near-best bases provide a
significant increase in computational efficiency
with reductions in memory, flops, and time while
nevertheless maintaining similar coding efficiency
with comparable reconstruction errors measured by
l^p-norms. Finally, a new compression scheme called
parameterized model coding is introduced and
demonstrated with results showing better compression
than standard scalar quantization coding at
comparable levels of distortion.",
}
@Book{teo:computational,
title = "Computational Signal Processing with Wavelets",
author = "A. Teolis",
publisher = "Springer-Verlag",
year = "1997",
pages = "332",
keywords = "Introduction * Mathematical Preliminaries * Signal
Representation and Frames * Continuous Wavelet
Transform * Discrete Wavelet Transform * Non-orthogonal
Wavelet Transform * Wavelet Signal Processing * World
Wide Web Access",
abstract = "Computational Signal Processing with Wavelets examines
both theoretical and practical aspects of computational
signal processing using wavelets. Theoretically, an
emphasis is placed on balancing the accessibility of
the material with the level of mathematical rigor which
sacrifices as little as possible of both.
Computationally, wavelet signal processing algorithms
are presented and applied to signal compression, noise
suppression, and signal identification. Numerical
illustrations of these computational techniques are
further provided with interactive software (MATLAB) via
an internet accessible WEB site. Starting from basic
principles of signal representation with atomic
functions, a mathematically well founded theory of the
discretization of analog signals is developed. General
families are specialized to wavelet families and the
discrete representation are specialized to generally
non-orthogonal wavelet transforms. The theory leads
naturally to the computer implementation of the
non-orthogonal wavelet transform. Specific topics
covered include general signal representation,
continuous and discrete Fourier transforms, orthonormal
and biorthogonal bases, frames, wavelet frames and
frame reconstruction, discrete wavelet transform,
multi-resolution analysis, orthonormal wavelets,
continuous wavelet transform, non-orthogonal wavelet
transform, and wavelet based signal processing
algorithms for compression, noise suppression, and
identification. The discussion is at the level of a
senior or beginning graduate student level and is
accessible to signal processing professionals and
practicioners. Dissemination of the material is
provided by a hybrid combination of traditional (text)
and non-traditional (internet and electronic) media.",
}
@Article{tet-kri:ocean,
title = "{SAR} Ocean Image Representation Using Wavelets",
author = "Joseph G. Teti and H. N. Kritikos",
journal = IEEETGRS,
volume = "30",
number = "5",
year = "1992",
pages = "1089--1094",
abstract = "The utility of wavelet analysis as a tool for
geophysical research is examined using both continuous
and discrete versions of the wavelet transform. In both
cases, waveform decomposition and reconstruction is
possible using somewhat different computational
procedures. The theoretical background of each
procedure is briefly described and applied using a
specific 'wavelet'. The wavelet used is based on a
Gaussian function, and provides simultaneous
time-frequency (or space-wavenumber) localization that
meets the lower limit of the uncertainty principle. A
representation of this type is ideally suited for the
analysis of waveforms that arise from nonstationary
processes. The properties of wavelet analysis are
examined by expanding an FM-chirp waveform and azimuth
cuts taken from two different SAR ocean images. The
performance and ease of implementation are compared for
the continuous and discrete formulations, and the
effects of filtering in wavelet phase space using the
discrete case are also examined.",
}
@Article{tew-kim:correlation,
title = "Correlation Structure of the Discrete Wavelet
Coefficients of Fractional {B}rownian Motion",
author = "A. H. Tewfik and M. Kim",
journal = IEEETIT,
volume = "38",
number = "2",
year = "1992",
pages = "904--909",
abstract = "It is shown that the discrete wavelet coefficients of
fractional Brownian motion at different scales are
correlated and that their auto- and cross-correlation
functions decay hyperbolically fast at a rate much
faster than that of the autocorrelation of the
fractional Brownian motion itself. The rate of decay of
the correlation function in the wavelet domain is
primarily determined by the number of vanishing moments
of the analyzing wavelet.",
}
@Book{tit:book,
title = "The Theory of Functions",
author = "E. C. Titchmarsh",
publisher = "Oxford University Press",
address = "Oxford",
edition = "2",
year = "1939",
pages = "454",
}
@Article{tor-com:practical,
title = "A Practical Guide to Wavelet Analysis",
author = "Christopher Torrence and Gilbert P. Compo",
journal = BAMetS,
volume = "79",
number = "1",
year = "1998",
pages = "61--78",
URL = "http://paos.colorado.edu/research/wavelets/",
keywords = "",
abstract = "A practical step-by-step guide to wavelet analysis is
given, with examples taken from time series of the El
Nino-Southern Oscillation (ENSO). The guide includes a
comparison to the windowed Fourier transform, the
choice of an appropriate wavelet basis function, edge
effects due to finite-length time series, and the
relationship between wavelet scale and Fourier
frequency. New statistical significance tests for
wavelet power spectra are developed by deriving
theoretical wavelet spectra for white and red noise
processes and using these to establish significance
levels and confidence intervals. It is shown that
smoothing in time or scale can be used to increase the
confidence of the wavelet spectrum. Empirical formulas
are given for the effect of smoothing on significance
levels and confidence intervals. Extensions to wavelet
analysis such as filtering, the power Hovmöller,
cross-wavelet spectra, and coherence are described. The
statistical significance tests are used to give a
quantitative measure of changes in ENSO variance on
interdecadal timescales. Using new datasets that extend
back to 1871, the Nino3 sea surface temperature and the
Southern Oscillation index show significantly higher
power during 1880-1920 and 1960-90, and lower power
during 1920-60, as well as a possible 15-yr modulation
of variance. The power Hovmöller of sea level pressure
shows significant variations in 2--8-yr wavelet power
in both longitude and time.",
}
@Unpublished{tor-web:interdecadal,
title = "Interdecadal Changes in the {ENSO}-Monsoon System",
author = "Christopher Torrence and Peter J. Webster",
journal = JC,
volume = "12",
number = "8",
year = "1999",
pages = "2679--2690",
URL = "http://www.cgd.ucar.edu/~torrence/interdec/",
keywords = "",
abstract = "The El Nino-Southern Oscillation (ENSO) and Indian
monsoon are shown to have undergone significant
interdecadal changes in variance and coherency over
the last 125 years. Wavelet analysis is applied to
indexes of equatorial Pacific sea surface
temperature (Nino3 SST), the Southern Oscillation
index, and all-India rainfall. Time series of 2-7-yr
variance indicate intervals of high ENSO-monsoon
variance (1875-1920 and 1960-90) and an interval of
low variance (1920-60). The ENSO-monsoon variance
also contains a modulation of ENSO-monsoon
amplitudes on a 12-20-yr timescale.The annual-cycle
(1 yr) variance time series of Nino3 SST and Indian
rainfall is negatively correlated with the
interannual ENSO signal. The 1-yr variance is larger
during 1935-60, suggesting a negative correlation
between annual-cycle variance and ENSO variance on
interdecadal timescales.The method of wavelet
coherency is applied to the ENSO and monsoon
indexes. The Nino3 SST and Indian rainfall are found
to be highly coherent, especially during intervals
of high variance. The Nino3 SST and Indian rainfall
are approximately 180 degrees out of phase and show
a gradual increase in phase difference versus
Fourier period. All of the results are shown to be
robust with respect to different datasets and
analysis methods.",
}
@Article{tor-web:persistence,
title = "The Annual Cycle of Persistence in the {E}l
{N}i\~no-{S}outhern {O}scillation",
author = "Christopher Torrence and Peter J. Webster",
journal = QJRMS,
volume = "125",
number = "",
year = "1998",
pages = "1985--2004",
URL = "http://www.cgd.ucar.edu/~torrence/barrier/",
keywords = "El Ni\~no-Southern Oscillation, Predictability,
Interdecadal Variability",
abstract = "A spring `predictability barrier' exists in both
data and models of the El Ni\~no-Southern
Oscillation (ENSO) phenomenon. In statistical
analyses this barrier manifests itself as a drop-off
in monthly persistence (lagged correlation) while in
coupled ocean-atmosphere models it appears as a
decrease in forecast skill. The persistence barrier
for ENSO indices is investigated using historical
sea surface temperature and sea level pressure
data. Simple statistical models are used to show
that the persistence barrier occurs because the
boreal spring is the transition time from one
climate state to another, when the `signal-to-noise'
of the system is lowest and the system is most
susceptible to perturbations. The strength of the
persistence barrier is shown to depend on the degree
of phase locking of the ENSO to the annual
cycle. The phase locking of the ENSO to the annual
cycle, as well as the ENSO variance, is shown to
vary on interdecadal time scales. During 1871--1920
and 1960--1990 the ENSO variance was high, while
during 1920--1950 the ENSO variance was low. Using
wavelet analysis, this interdecadal variability in
ENSO is shown to be correlated with changes in
Indian summer monsoon strength. Finally, the change
in persistence barrier strength between 1960--1979
and 1980--1995 is related to changes in the phase
locking of ENSO to the annual cycle. These changes
in persistence and phase locking appear to be
related to the increased forecast skill seen in
recent coupled ocean-atmosphere models.",
}
@PhdThesis{tor:thesis,
title = "The El Ni\~no-Southern Oscillation: Interannual
Predictability and Interdecadal Variability",
author = "Christopher Torrence",
school = "University of Colorado at Boulder",
year = "1997",
}
@Article{tre-and:turbulence,
title = "On wavelet analysis of nonstationary turbulence",
author = "Beorge Trevi{\~n}o and Edgar L. Andreas",
journal = BLM,
volume = "81",
number = "3-4",
year = "1996",
pages = "271--288",
keywords = "coherent structures, forest canopy, transforms,
cascade, motions",
abstract = "Wavelets are new tools for turbulence analysis that
are yielding important insights into boundary-layer
processes. Wavelet analysis, however, has some as yet
undiscussed limitations: failure to recognize these can
lead to misinterpretation of wavelet analysis results.
Here we discuss some limitations of wavelet analysis
when applied to nonstationary turbulence. Our main
point is that the analysis wavelet must be carefully
matched to the phenomenon of interest, because wavelet
coefficients obscure significant information in the
signal being analyzed. For example, a wavelet that is a
second-difference operator can provide no information
on the linear trend in a turbulence signal. Wavelet
analysis also yields no meaningful information about
nonlinear behavior in a signal - contrary to claims in
the literature - because, at any instant, a wavelet is
a single-scale operator, while nonlinearity involves
instantaneous interactions among many scales.",
}
@InCollection{tri:adaptive,
title = "Adaptive Density Estimation",
author = "K. Tribouley",
pages = "385--395",
crossref = "ant-opp:wavelets",
URL = "",
abstract = "",
}
@Article{tri:practical,
title = "Practical estimation of multivariate densities using
wavelet methods",
author = "K. Tribouley",
journal = SN,
volume = "49",
number = "1",
year = "1995",
pages = "41--62",
abstract = "This paper describes a practical method for estimating
multivariate densities using wavelets. As in kernel
methods, wavelet methods depend on two types of
parameters. On the one hand we have a functional
parameter: the wavelet [phi] (comparable to the kernel
K) and on the other hand we have a smoothing parameter:
the resolution index (comparable to the bandwidth h).
Classically, we determine the resolution index with a
cross-validation method. The advantage of wavelet
methods compared to kernel methods is that we have a
technique for choosing the wavelet [phi] among a fixed
family. Moreover, the wavelets method simplifies
significantly both the theoretical and the practical
computations.",
keywords = "Density estimation cross validation wavelet
orthonormal bases Besov spaces",
}
@Article{tso-kum-els-tso:dna,
journal = PRE,
volume = "53",
number = "2",
year = "1997",
pages = "1828--1834",
title = "{W}avelet analysis of {DNA} sequences",
author = "A. A. Tsonis and P. Kumar and J. B. Elsner and P. A.
Tsonis",
abstract = "In this paper we use wavelet analysis in order to
probe the localized structure of DNA sequences. We
demonstrate that, unlike other conventional approaches,
wavelets are able to decompose seemingly homogeneous
regions in noncoding sequences into smaller distinct
regions that obey their own repetition and construction
rules. The significance of this result to gene
evolution is discussed.",
keywords = "coding sequences, sampling theory, evolution,
propagation, gene",
}
@Article{tur-hal:interpolation,
title = "Interpolation Methods for Nonlinear Wavelet Regression
with Irregularly Spaced Design",
author = "Berwin A. Turlach and Peter Hall",
journal = "AS",
volume = "25",
number = "5",
year = "1997",
email = "berwin@alphasun.anu.edu.au",
abstract = "We suggest and discuss interpolation methods that
enable nonlinear wavelet estimators to be employed with
stochastic design, or non-dyadic regular design, in
problems of nonparametric regression. This approach
allows relatively rapid computation, involving dyadic
approximations to wavelet-after-interpolation
techniques. New types of interpolation are described,
enabling first-order variance reduction at the expense
of second-order increases in bias. The effect of
interpolation on threshold choice is addressed, and
appropriate thresholds are suggested for error
distributions with as few as four finite moments. A
concise account of mean squared error properties is
given for interpolation-based wavelet estimators
applied to piecewise-smooth functions.",
}
@Article{uns-ald:biomedical,
journal = PIEEE,
volume = "84",
number = "4",
year = "1996",
pages = "626--638",
title = "{A} review of wavelets in biomedical applications",
author = "M. Unser and A. Aldroubi",
abstract = "In this paper we present an overview of the various
uses of the wavelet transform (WT) in medicine and
biology. We start by describing the wavelet properties
that are the most important for biomedical
applications. In particular, we provide an
interpretation of the continuous wavelet transform
(CWT) as a prewhitening multiscale matched filter. Me
also briefly indicate the analogy between the WT and
some of the biological processing that occurs in the
early components of the auditory and visual system. We
then review the rises of the WT for the analysis of 1-D
physiological signals obtained by phonocardiography,
electrocardiography (ECC), and electroencephalography
(EEG), including evoked response Next, we provide a
survey of recent wavelet developments in medical
imaging. These include biomedical image processing
algorithms (e.g., noise reduction, image enhancement,
and detection of microcalcifications in mammograms),
image reconstruction and acquisition schemes
(tomography, and magnetic resonance imaging (MRI)), and
multiresolution methods for the registration and
statistical analysis of functional images of the brain
(positron emission tomography (PET) and functional MRI
(fMRI)). In each case, we provide the reader with some
general background information and a brief explanation
of how the methods work.",
}
@Article{uns-the-ald:shift,
title = "Shift-orthogonal wavelet bases",
author = "Unser, M. and Thevenaz, P. and Aldroubi, A.",
journal = IEEETSP,
volume = "46",
number = "7",
year = "1998",
pages = "1827--1836",
keywords = "multiresolution approximations ondelettes spaces",
abstract = "Shift-orthogonal wavelets are a new type of
multiresolution wavelet bases that are orthogonal with
respect to translation (or shifts) within one level but
not with respect to dilations across scales. In this
paper, we characterize these wavelets and investigate
their main properties by considering two general
construction methods. In the first approach, we start
by specifying the analysis and synthesis function spaces
and obtain the corresponding shift-orthogonal basis
functions by suitable orthogonalization. In the second
approach, we take the complementary view and start from
the digital filterbank. We present several illustrative
examples, including a hybrid version of the
Battle-Lemarie spline wavelets. We also provide
filterbank formulas for the fast wavelet algorithm. A
shift-orthogonal wavelet transform is closely related to
an orthogonal transform that uses the same primary
scaling function; both transforms have essentially the
same approximation properties. One experimentally
confirmed benefit of relaxing the interscale orthogonality
requirement is that we can design wavelets that decay
faster than their orthogonal counterpart.",
}
@TechReport{uyt-bul:red-black,
title = "The Red-Black Wavelet Transform",
author = "Geert Uytterhoeven and Adhemar Bultheel",
number = "271",
institution = "Department of Computer Science, Katholieke
Universiteit Leuven",
year = "1997",
URL = "http://www.cs.kuleuven.ac.be/publicaties/rapporten/tw/TW271.ps.gz",
}
@TechReport{van-bro-fea:long-memory,
title = "Wavelet Analysis of Long-memory Processes",
author = "Marina Vannucci and Philip J. Brown and Tom Fearn",
institution = "Institute of Mathematics and Statistics, University of
Kent at Canterbury",
note = "UKC/IMS/98/22",
year = "1998",
email = "M.Vannucci@ukc.ac.uk",
URL = "",
}
@Article{van-cor:covariance,
title = "Covariance Structure of Wavelet Coefficients:
{T}heory and Models in a Bayesian Perspective",
author = "Marina Vannucci and Fabio Corradi",
journal = JRSSB,
volume = "?",
number = "?",
year = "1999",
pages = "???--???",
email = "mvannucci@stat.tamu.edu, corradi@stat.ds.unifi.it",
URL = "http://stat.tamu.edu/~mvannucci/webpages/papers/wjrssb.ps",
keywords = "",
abstract = "",
}
@InCollection{van-cor:dependence,
title = "Modeling Dependence in the Wavelet Domain",
author = "Marina Vannucci and Fabio Corradi",
pages = "???--???",
crossref = "mul-vid:biwbm",
URL = "http://stat.tamu.edu/~mvannucci/webpages/papers/deprior.ps",
keywords = "",
abstract = "",
}
@Article{van-vid:preventing,
title = "Preventing the {D}irac disaster: {W}avelet based
density estimation",
author = "Marina Vannucci and Brani Vidakovic",
journal = JISS,
volume = "6",
number = "2",
year = "1999",
pages = "???--???",
URL = "http://stat.tamu.edu/~mvannucci/webpages/paper/wjiss.ps",
}
@PhdThesis{van:thesis,
title = "On the Application of Wavelets in Statistics",
author = "Marina Vannucci",
school = "Dipartimento di Statistica ``G. Parenti'',
University of Florence, Italy",
year = "1996",
postscript = "http://www.isds.duke.edu/~brani/wp/marina.ps",
note = "In Italian",
}
@Unpublished{vei-abr:constancy,
title = "A Statistical Test for the Time Constancy of Scaling
Exponents",
author = "Darryl Veitch and Patrice Abry",
year = "1999",
note = "Submitted for publication",
URL = "http://www.serc.rmit.edu.au/~darryl/A4.ps",
}
@Article{vei-abr:joint,
title = "A wavelet based joint estimator of the parameters of
long-range dependence",
author = "Darryl Veitch and Patrice Abry",
journal = IEEETIT,
volume = "45",
number = "3",
year = "1999",
pages = "878--897",
URL = "http://www.serc.rmit.edu.au/~darryl/A3.ps",
keywords = "Hurst parameter long-range dependence packet traffic
parameter estimation telecommunications networks
time-scale analysis wavelet decomposition",
abstract = "A joint estimator is presented for the two
parameters that define the long-range dependence
phenomenon in the simplest case. The estimator is
based on the coefficients of a discrete wavelet
decomposition, improving a recently proposed
wavelet-based estimator of the scaling parameter
[4], as well as extending it to include the
associated power parameter. An important feature is
its conceptual and practical simplicity, consisting
essentially in measuring the slope and the intercept
of a linear fit after a discrete wavelet transform
is performed, a very fast (O(n)) operation. Under
well-justified technical idealizations the estimator
is shown to be unbiased and of minimum or close to
minimum variance for the scale parameter, and
asymptotically unbiased and efficient for the second
parameter. Through theoretical arguments and
numerical simulations it is shown that in practice,
even for small data sets, the bias is very small and
the variance close to optimal for both
parameters. Closed-form expressions are given for
the covariance matrix of the estimator as a function
of data length, and are shown by simulation to be
very accurate even when the technical idealizations
are not satisfied, Comparisons are made against two
maximum-likelihood estimators. In terms of
robustness and computational cost the wavelet
estimator is found to be clearly superior and
statistically its performance is comparable, We
apply the tool to the analysis of Ethernet
teletraffic data, completing an earlier study on the
scaling parameter alone.",
}
@Article{vel-ulr:annealing,
title = "Simulated annealing wavelet estimation via
fourth-order cumulant matching",
author = "D. R. Velis and T. J. Ulrych",
journal = "Geophysics",
volume = "61",
number = "6",
year = "1996",
pages = "1939--1948",
keywords = "deconvolution, coefficients, gaussianity, phase",
abstract = "The fourth-order cumulant matching method has been
developed recently for estimating a mixed-phase wavelet
from a convolutional process. Matching between the
trace cumulant and the wavelet moment is done in a
minimum mean-squared error sense under the assumption
of a non-Gaussian, stationary, and statistically
independent reflectivity series. This leads to a highly
nonlinear optimization problem, usually solved by
techniques that require a certain degree of
linearization, and that invariably converge to the
minimum closest to the initial model. Alternatively, we
propose a hybrid strategy that makes use of a simulated
annealing algorithm to provide reliability of the
numerical solutions by reducing the risk of being
trapped in local minima. Beyond the numerical aspect,
the reliability of the derived wavelets depends
strongly on the amount of data available. However, by
using a multidimensional taper to smooth the trace
cumulant, we show that the method can be used even in a
trace-by-trace implementation, which is very important
from the point of view of stationarity and consistency.
We demonstrate the viability of the method under
several reflectivity models. Finally, we illustrate the
hybrid strategy using marine and held real data
examples. The consistency of the results is very
encouraging because the improved cumulant matching
strategy we describe can be effectively used with a
limited amount of data.",
}
@Book{vet-kov:wavelets,
title = "Wavelets and Subband Coding",
author = "Martin Vetterli and Jelena Kova{\v{c}}evi{\'c}",
year = "1995",
publisher = "Prentice Hall PTR",
address = "New Jersey",
URL = "http://www.prenhall.com/allbooks/ptr_0130970808.html",
keywords = "discrete-time case, or filter banks; development of
wavelets; continuous wavelet and local Fourier
transforms; efficient algorithms for filter banks and
wavelet computations; and signal compression",
}
@TechReport{vid-kat-alb:multiscale,
title = "Multiscale Denoising of Self Similar Processes",
author = "Brani Vidakovic and Gabriel Katul and John
Albertson",
number = "00-02",
institution = "Institute of Statisics and Decision Sciences, Duke
University",
year = "2000",
URL = "http://ftp.isds.duke.edu/WorkingPapers/00-02.ps",
abstract = "A practical limitation to investigating
self-similarity in geophysical phenomena from their
measured state variables is that measured signals
are typically convolved with instrumentation noise
at multiple scales. This study develops and tests a
multiscale Bayesian model (BEFE) for separating a
$1/f$-like signal from inherent instrumentation
noise and contrasts its performance to the
Wiener-type (WAS) and Fourier amplitude (FAS)
shrinkage methods. The novel feature in BEFE is that
the separation is performed in the wavelet domain
and involves the use of a Bayesian inference
approach guided by existing theoretical power-laws
in the filtered signal energy spectrum. We contrast
the performance of all three methods for synthetic
fractional Brownian motion ({\it fBm}) signals and
turbulent velocity time series collected in the
atmospheric boundary layer. A discussion on the
advantages and disadvantages of each method is also
presented, particularly when the process is not
exactly an {\it fBm}.",
}
@Article{vid-loz:time-dependent,
title = "On time-dependent wavelet denoising",
author = "Vidakovic, B. and Lozoya, C. B.",
journal = IEEETSP,
volume = "46",
number = "9",
year = "1998",
pages = "2549--2554",
keywords = "denoising image processing wavelet shrinkage",
abstract = "In this correspondence, we address the shrinkage of
wavelet coefficients and induced denoising in the
time domain by taking into consideration the
`time' behavior of a noisy signal. We illustrate
our time adaptation paradigm in a thresholding
procedure utilizing Bayesian hypothesis tests. Both
one-dimensional (1-D) and two-dimensional (2-D)
signals are considered in examples to motivate and
implement our method.",
}
@Unpublished{vid-mul:kids,
title = "Wavelets for Kids: Tutorial Introduction",
author = "Brani Vidakovi{\'c} and Peter M{\"u}ller",
note = "Institute of Statisics and Decision Sciences, Duke
University",
year = "1994",
email = "brani@isds.duke.edu, pm@isds.duke.edu",
URL = "http://www.isds.duke.edu/~brani/papers/wav4kidsA.ps",
}
@Article{vid:bayes,
title = "Nonlinear wavelet shrinkage with {B}ayes rules and
{B}ayes factors",
author = "Brani Vidakovic",
journal = JASA,
volume = "93",
number = "441",
year = "1998",
pages = "173--179",
URL = "http://www.isds.duke.edu/~brani/papers/WavShrinkBF.ps",
keywords = "Bayes model denoising thresholding wavelet regression",
abstract = "Wavelet shrinkage, the method proposed by the
seminal work of Donoho and Johnstone is a
disarmingly simple and efficient way of denoising
data. Shrinking wavelet coefficients was proposed
from several optimality criteria. In this article a
wavelet shrinkage by coherent Bayesian inference in
the wavelet domain is proposed. The methods are
tested on standard Donoho- Johnstone test
functions.",
}
@Book{vid:book,
title = "Statistical Modeling by Wavelets",
author = "Brani Vidakovic",
publisher = "John Wiley \& Sons",
address = NY,
year = "1999",
pages = "381",
ISBN = "0471293652",
URL = "http://www.isds.duke.edu/~brani/Wiley.html",
keywords = "",
abstract = "",
}
@Article{von-nas-kro:adaptive,
title = "Wavelet processes and adaptive estimation of the
evolutionary wavelet spectrum",
author = "Rainier {von Sachs} and Guy P. Nason and Gerald
Kroisandt",
journal = JRSSB,
volume = "62",
number = "2",
year = "2000",
pages = "271--292",
URL = "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/StanTechRep516.ps.gz",
abstract = "",
}
@InCollection{von-nas-kro:spectral,
title = "Spectral representation and estimation for locally
stationary wavelet processes",
author = "Rainier {von Sachs} and Guy P. Nason and Gerald
Kroisandt",
booktitle = "Spline Functions and the Theory of Wavelets",
editor = "S. Dubuc and G. Deslauriers",
series = "CRM Proceedings \& Lecture Notes",
publisher = "American Mathematical Society",
address = "Montreal, Canada",
volume = "18",
year = "1999",
pages = "381--397",
URL = "http://playfair.Stanford.EDU/reports/rvs/vSNK.ps.gz",
}
@Article{von-neu:stationarity,
title = "A Wavelet-based Test for Stationarity",
author = "Rainier {von Sachs} and Michael H. Neumann",
journal = JTSA,
volume = "",
number = "",
year = "2000",
pages = "--",
URL = "http://playfair.Stanford.EDU/reports/rvs/Stattest.ps.gz",
}
@Article{von-sch:evolutionary,
title = "Wavelet smoothing of evolutionary spectra by
non-linear thresholding",
author = "Rainier {von Sachs} and Kai Shneider",
journal = ACHA,
volume = "3",
year = "1996",
pages = "268--282",
URL = "http://www.mathematik.uni-kl.de/~wwwtecm/preprints/reports/report_106.ps.gz",
abstract = "We consider wavelet estimation of the time-dependent
(evolutionary) power spectrum of a locally
stationary time series in a model which was recently
introduced by Dahlhaus [2]. Allowing for departures
from stationary proves useful for modelling, e.g.,
transient phenomena, quasi-oscillating behaviour or
spectrum modulation. In contrast to classical
parametric and nonparametric (linear) approaches we
use nonlinear thresholding of the empirical wavelet
coefficients of the evolutionary spectrum. We show
how these techniques allow for both adaptively
reconstructing the local structure in the
time-frequency plane and for denoising the resulting
estimates. To this end a threshold choice is derived
which is motivated by minimax properties w.r.t. the
integrated mean squared error. Our approach is based
on a 2-d orthogonal wavelet transform modified by
using a cardinal Lagrange interpolation function on
the finest scale. As an example, we apply our
procedure to a time-varying spectrum motivated from
mobile radio propagation.",
}
@Article{von:modelling,
title = "Modelling and Estimation of the Time-varying
Structure of Nonstationary Time Series",
author = "Rainier {von Sachs}",
journal = "Brazilian Journal of Probability and Statistics",
volume = "10",
number = "2",
year = "1996",
pages = "181--204",
URL = "http://playfair.Stanford.EDU/reports/rvs/brazilpaper.ps.gz",
}
@TechReport{von:nonparametric,
title = "Nonparametric Wavelet Methods for Nonstationary Time
Series",
author = "Rainier {von Sachs}",
number = "98/19",
year = "1998",
institution = "Institut de Statistique, Universit{\'e} Catholique
de Louvain",
URL = "http://www.stat.ucl.ac.be/dp/dp98/9819.ps",
}
@Article{wal-con:matching,
title = "Matching pursuit by undecimated discrete wavelet
transform for non-stationary time series of
arbitrary length",
author = "Andrew T. Walden and A. Contreras Cristan",
journal = SC,
volume = "8",
number = "3",
year = "1998",
pages = "205--219",
URL = "http://www.ma.ic.ac.uk/statistics/links/atw.link/matching-pursuit-TR-96-02.ps",
keywords = "",
abstract = "",
}
@Article{wal-con:shock,
title = "The phase-corrected undecimated discrete wavelet
packet transform and the recurrence of high latitude
interplanetary shock waves",
author = "Andrew T. Walden and Alberto Contreras Cristan",
journal = PRSLA,
volume = "454",
number = "1976",
year = "1998",
pages = "2243--2266",
keywords = "wavelet packet transform wavelet phase
non-stationary time series Ulysses spacecraft
solar magnetic field heliospheric magnetic-field
fourier-analysis representation algorithms ulysses.",
URL = "http://www.ma.ic.ac.uk/statistics/links/atw.link/phase-corrected-TR-97-03.ps",
abstract = "This paper is concerned with the development and
application of the phase-corrected maximal overlap
discrete wavelet packet transform (MODWPT). The
discrete cyclic filtering steps of the MODWPT are
fully explained. Energy preservation is proven. With
filter coefficients chosen from Daubechies's least
asymmetric class, the optimum time shifts to apply
to ensure approximate zero phase filtering at every
level of the MODWPT are studied, and applied to the
wavelet packet coefficients to give phase
corrections which ensure alignment with the original
time series. Also, the time series values at each
time are decomposed into details associated with
each frequency band, and these line up perfectly
with features in the original time series since the
details are shown to arise through exact zero phase
filtering. The phase-corrected MODWPT is applied to
a non-stationary time series of hourly averaged
Southern Hemisphere solar magnetic field magnitude
data acquired by the Ulysses spacecraft. The
occurrence times of the shock waves previously
determined via manual pattern matching on the raw
data match those times in the time-frequency plot
where a broadband spectrum is obtained; in other
words, the phase-corrected MODWPT provides an
approach to picking the location of complicated
events. We demonstrate the superiority of the MODWPT
in interpreting timing information over two
competing methods, namely the cosine packet
transform (or 'local cosine transform'), and the
short-time Fourier transform."
}
@Article{wal-per-mcc:multitaper,
title = "Spectrum Estimation by Wavelet Thresholding of
Multitaper Estimators",
author = "Andrew T. Walden and Donald B. Percival and Emma J.
McCoy",
journal = IEEETSP,
volume = "46",
number = "12",
pages = "3153--3165",
year = "1998",
abstract = "Current methods for power spectrum estimation by
wavelet thresholding use the empirical wavelet
coefficients derived from the log periodogram.
Unfortunately, the periodogram is a very poor estimate
when the true spectrum has a high dynamic range and/or
is rapidly varying. In addition, because the
distribution of the log periodogram is markedly
non-Gaussian, special wavelet-dependent thresholding
schemes are needed. These difficulties can be
bypassed by starting with a multitaper spectrum
estimator. The logarithm of this estimator is close
to Gaussian distributed if a moderate number (greater
than or equal to 5) of tapers are used. In contrast to
the log periodogram, log multitaper estimates are not
approximately pairwise uncorrelated at the Fourier
frequencies, but the form of the correlation can be
accurately and simply approximated. For
scale-independent thresholding, the correlation acts
in accordance with the wavelet shrinkage paradigm to
suppress small-scale `noise spikes' while leaving
informative coarse scale coefficients relatively
unattenuated. This simple approach to spectrum
estimation is demonstrated to work very well in
practice. Additionally, the progression of the
variance of wavelet coefficients with scale can be
accurately calculated, allowing the use of
scale-dependent thresholds. This more involved
approach also works well in practice but is not
uniformly preferable to the scale-independent
approach.",
}
@Book{wal:orthogonal,
title = "Wavelets and Other Orthogonal Systems with
Applications",
author = "Gilbert G. Walter",
publisher = "CRC Press Inc.",
address = "Boca Raton",
pages = "272",
year = "1994",
URL = "http://www.crcpress.com/prods/7878.htm",
abstract = "This book makes accessible to both mathematicians and
engineers important elements of the theory,
construction, and application of orthogonal wavelets.
It is integrated with more traditional orthogonal
series, such as Fourier series and orthogonal
polynomials. It treats the interaction of both with
generalized functions (delta functions), which have
played an important part in engineering theory but
whose rules are often vaguely presented. Unlike most
other books that are excessively technical, this
text/reference presents the basic concepts and examples
in a readable form. Much of the material on wavelets
has not appeared previously in book form. Applications
to statistics, sampling theorems, and stochastic
processes are given. In particular, the close affinity
between wavelets and sampling theorems is explained and
developed.",
}
@Unpublished{wan-cav-son:self-similarity,
title = "Self-similarity index estimation via wavelets for
locally self-similar processes",
author = "Yazhen Wang and Joseph E. Cavanaugh and Changyong
Song",
year = "1997",
note = "Department of Statistics, University of Missouri",
}
@Article{wan-zho:aseismic,
title = "Aseismic designs based on artificial simulations -
{H}ow to achieve chirplet-based signal approximation
with a strong earthquake ground-model",
author = "Jun-Jie Wang and Jing Zhou",
journal = IEEESPM,
volume = "16",
number = "2",
month = "March",
year = "1999",
pages = "94--99",
keywords = "motion",
}
@Unpublished{wan:change-curve,
title = "Change curve estimation via wavelets",
author = "Yazhen Wang",
institution = "Department of Statistics, University of Missouri",
year = "1997",
note = "{\em Journal of the American Statistical Association},
to be published in 1998",
}
@Article{wan:indirect,
title = "Change-points via wavelets for indirect data",
author = "Yazhen Wang",
journal = SSin,
volume = "9",
number = "1",
year = "1999",
pages = "103--117",
abstract = "This article studies change-points of a function for
noisy data observed from a transformation of the
function. The proposed method uses a
wavelet-vaguelette decomposition to extract
information about the wavelet transformation of the
function from the data and then detect and estimate
change-points by the wavelet
transformation. Asymptotic theory for the detection
and estimation is established. A simulated example
is carried out to illustrate the method.",
}
@Article{wan:jump,
title = "Jump and sharp cusp detection by wavelets",
author = "Yazhen Wang",
journal = BKA,
volume = "82",
number = "2",
year = "1995",
pages = "385--397",
abstract = "A method proposed to detect jumps and sharp cusps in
a function which is observed with noise, by checking
if the wavelet transformation of the data has
significantly large absolute values across fine
scales. Asymptotic theory is established and
practical implementation is discussed. The method is
tested on simulated examples, and applied to stock
market return data.",
}
@Article{wan:long-range,
title = "Function estimation via wavelet shrinkage for
long-memory data",
author = "Yazhen Wang",
journal = AofS,
volume = "24",
number = "2",
year = "1996",
pages = "466--484",
}
@Article{wei-bov:enhancement,
title = "Enhancement of compressed images by optimal
shift-invariant wavelet packet basis",
author = "Wei, D. and Bovik, A. C.",
journal = JVCIR,
volume = "9",
number = "1",
year = "1998",
pages = "15--24",
keywords = "compactly supported wavelets coded images transform
reduction algorithms bases",
abstract = "A novel postprocessing method based on the optimal
shift-invariant wavelet packet (SIWP) representation
and wavelet shrinkage is proposed to enhance
compressed images. At the encoder, the optimal (in
the mean square error sense) SIWP basis is searched
using a fast optimization algorithm and the location
of the best basis in the entire SIWP library is
transmitted as overhead information to the
decoder. The selected basis is jointly optimal in
terms of both the time-frequency tiling and the
relative time-domain offset (or shift) between a
signal and its wavelet packet representation. After
the decoder reconstructs the compressed image, the
postprocessor performs wavelet shrinkage using the
optimal basis. Due to its powerful adaptability, the
method is shown to achieve a better trade-off
between enhancement performance and decoder
complexity than both the orthonormal wavelet
transform and the undecimated wavelet
transform-based methods.",
}
@Article{wei-dix:underwater,
journal = JAcSA,
volume = "101",
number = "1",
year = "1997",
pages = "377--383",
title = "{W}avelet-based denoising of underwater acoustic
signals",
author = "L. G. Weiss and T. L. Dixon",
abstract = "Underwater environmental measurements of the ocean
require signals that are free from unwanted backscatter
and clutter. Removing these unwanted signal components
usually amounts to applying some form of filtering
technique such as a high pass filter, a bandpass
filter, a Wiener filter, etc. These approaches however
are limited in their abilities to remove acoustic
returns that vary spectrally. This paper presents a
multiresolution approach to removing unwanted
backscatter from high-frequency underwater acoustic
signals and compares it to high pass filtering of the
same signals. The filtering approach presented applies
wavelet transforms for signal recovery and denoising of
high-frequency acoustic signals. It is shown that by
computing a wavelet transform of the returned signals,
applying a denoising technique, and then reconstructing
the signal, additional unwanted backscatter can be
removed.",
keywords = "scattering",
}
@Unpublished{wei:invariance,
title = "Translation Invariance and the Wavelet Transform",
author = "John Weiss",
year = "1993",
note = "Applied Mathematics Group",
URL = "http://www.tiac.net/users/nurit/trep3/trep3.html",
keywords = "wavelet transform, translation invariance, best basis,
transient detection",
abstract = "A translation invariant wavelet transform algorithm is
defined. The algorithm is an extension of the best
basis approach and can be used to define translation
invariant best bases and wavelet transforms. The
computational cost is a factor of $m$ greater than the
usual algorithms, where $m$ is the multiplier of the
wavelet system. Some applications to transient
detection are presented. A general form of an invariant
wavelet transform is presented. This transform is shown
to be invariant under a large group of symmetries
described, most naturally, by the g-circulant
transformations. The symmetries include translation and
time-reversal of a periodic data vector. In our
construction the expansion coefficients of g-circulant
transformations of a data vector areshown to be simply
related by periodic shifts of their expansion
coefficients. Therefore, under g-circulant
transformations the numerical values and ordering are
invariant.",
}
@InCollection{wey-war:de-noising,
title = "De-noising using wavelets and cross validation",
author = "N. Weyrich and G. T. Warhola",
booktitle = "Recent Developments in Approximation Theory,
Wavelets and Applications",
editor = "S. P. Singh",
publisher = "Kluwar",
address = "Boston, MA",
year = "1995",
pages = "523--532",
}
@Article{wey-war:shrinkage,
title = "Wavelet shrinkage and generalized cross validation
for image denoising",
author = "N. Weyrich and G. T. Warhola",
journal = IEEETIP,
volume = "7",
number = "1",
pages = "82--90",
year = "1998",
abstract = "We present a denoising method based on wavelets and
generalized cross validation and apply these methods
to image denoising, We describe the method of
modified wavelet reconstruction and show that the
related shrinkage parameter vector can be chosen
without prior knowledge of the noise variance by
using the method of generalized cross validation, By
doing so, we obtain an estimate of the shrinkage
parameter vector and, hence, the image, which is
very close to the best achievable mean-squared error
result-that given by complete knowledge of the
underlying clean image.",
}
@Unpublished{whi-etal:lmwnr,
title = "Testing for Homogeneity of Variance in Time Series:
{L}ong Memory, Wavelets and the {N}ile {R}iver",
author = "Brandon Whitcher and Simon D. Byers and Peter
Guttorp and Donald B. Percival",
year = "1998",
note = "Submitted for publication",
URL = "http://www.eurandom.tue.nl/whitcher/papers/nile.ps",
keywords = "Cumulative sum of squares; Discrete wavelet
transform, Fractional difference process; Variance
change",
abstract = "We consider the problem of testing for homogeneity
of variance in a time series that has long memory
structure. We demonstrate that a test whose null
hypothesis is designed to be white noise can in fact
be applied, on a scale by scale basis, to the
discrete wavelet transform of long memory
processes. In particular, we show that evaluating a
normalized cumulative sum of squares test statistic
using critical levels appropriate for the null
hypothesis of white noise yields approximately the
same null hypothesis rejection rates when applied to
the discrete wavelet transform of samples from a
fractional difference process. The point at which
the test statistic, using the maximal overlap
discrete wavelet transform, achieves its maximum
value can be used to estimate the time of the
unknown variance change. We apply our proposed test
statistic on a time series of Nile River yearly
minimum water levels covering the years 622 to 1284
AD. The test confirms an inhomogeneity of variance
at short scales and identifies the change point
around 720 AD, which coincides closely with the
construction of a new device in 715 AD for measuring
Nile River water levels.",
}
@TechReport{whi-gut-per:background,
title = "Mathematical Background for Wavelet Estimators for
Cross-Covariance and Cross-Correlation",
author = "Brandon Whitcher and Peter Guttorp and Donald
B. Percival",
institution = "National Research Center for Statistics and the
Environment",
number = "38",
year = "1999",
URL = "http://www.eurandom.tue.nl/whitcher/papers/background.ps",
}
@Article{whi-gut-per:covariance,
title = "Wavelet Analysis of Covariance with Application to
Atmospheric Time Series",
author = "Brandon Whitcher and Peter Guttorp and Donald
B. Percival",
journal = JGRA,
volume = "",
number = "",
year = "2000",
pages = "",
note = "to appear",
URL = "http://www.eurandom.tue.nl/whitcher/papers/wavecov.ps",
keywords = "Confidence intervals; Cross-correlation;
Cross-covariance; Madden-Julian oscillation; Maximal
overlap discrete wavelet transform; Southern
Oscillation Index",
abstract = "Multi-scale analysis of univariate time series has
appeared in the literature at an ever increasing
rate. Here we introduce the multi-scale analysis of
covariance between two time series using the
discrete wavelet transform. The wavelet covariance
and wavelet correlation are defined and applied to
this problem as an alternative to traditional
cross-spectrum analysis. The wavelet covariance is
shown to decompose the covariance between two
stationary processes on a scale by scale
basis. Asymptotic normality is established for
estimators of the wavelet covariance and
correlation. Both quantities are generalized into
the wavelet cross-covariance and cross-correlation
in order to investigate possible lead/lag
relationships. A thorough analysis of
El-Ni\~no--Southern Oscillation events and the
Madden--Julian oscillation is performed using a 35+
year record. We show how potentially complicated
patterns of cross-correlation are easily decomposed
using the wavelet cross-correlation on a scale by
scale basis, where each wavelet cross-correlation
series is associated with a specific physical time
scale.",
}
@Article{whi-jen:aseg2000,
title = "Wavelet Estimation of a Local Long Memory Parameter",
author = "Brandon Whitcher and Mark J. Jensen",
journal = "Exploration Geophysics",
volume = "31",
number = "1 \& 2",
year = "2000",
pages = "89--98",
URL = "http://www.eurandom.tue.nl/whitcher/papers/ASEG2000.pdf",
keywords = "discrete wavelet transform, least-squares
regression, long-range dependence, time series,
wavelet variance.",
abstract = "Physical processes often exhibit long-range
dependence that vary and evolve over time. Various
techniques already exist in order to estimate global
long-range dependence. That is, these methods assume
the level of dependence does not vary over time and
hence, fail to adapt to any potential change in the
level of long-range dependence. The discrete wavelet
transform is well-localized in time-scale space and
thus, enables us to consistently estimate a local
measure of long-range dependence and the time
interval over which this estimate is constant. We
utilize the so-called `cone of influence'
(level-dependent support of the wavelet filter)
induced by the wavelet transform to define an
estimator of local variability - the time-dependent
wavelet variance. Using a fractionally integrated
autoregressive, moving average model, whose
differencing parameter changes over time, we
estimate the local differencing parameter at time
$t$ using a log-log linear relationship between the
time-dependent wavelet variance whose support
contains $t$ and the scale parameter of the wavelet
transform. Simulation studies demonstrate the
estimation procedure for a variety of time-varying
fractionally integrated autoregressive, moving
average processes and we also apply it to a
geophysical process.",
}
@Unpublished{whi-gut-per:multiple,
title = "Multiscale Detection and Location of Multiple
Variance Changes in the Presence of Long Memory",
author = "Brandon Whitcher and Peter Guttorp and Donald
B. Percival",
year = "1999",
note = "{\em Journal of Statistical Computation and
Simulation}, to appear",
URL = "http://www.eurandom.tue.nl/whitcher/papers/multiple.ps",
keywords = "",
abstract = "",
}
@Unpublished{whi:simulating,
title = "Simulating {G}aussian Stationary Processes with
Unbounded Spectra",
author = "Brandon Whitcher",
year = "1999",
note = "Tentatively accepted for publication in the {\em
Journal of Computational and Graphical Statistics}",
URL = "http://www.eurandom.tue.nl/whitcher/papers/sim.ps",
}
@PhdThesis{whi:thesis,
title = "Assessing Nonstationary Time Series Using Wavelets",
author = "Brandon Whitcher",
school = "University of Washington",
year = "1998",
postscript = "http://www.eurandom.tue.nl/whitcher/papers/thesis.ps.gz",
abstract = "The discrete wavelet transform has be used
extensively in the field of statistics, mostly in
the area of ``denoising signals'' or nonparametric
regression. This thesis provides a new application
for the discrete wavelet transform, assessing
nonstationary events in time series -- especially
long memory processes. Long memory processes are
those which exhibit substantial correlations between
events separated by a long period of
time. Departures from stationarity in these heavily
autocorrelated time series, such as an abrupt change
in the variance at an unknown location or ``bursts''
of increased variability, can be detected and
accurately located using discrete wavelet transforms
-- both orthogonal and overcomplete. A cumulative
sum of squares method, utilizing a
Kolomogorov--Smirnov-type test statistic, and an
information criterion method are investigated. By
analyzing a time series on a scale by scale basis,
each scale corresponding to a range of frequencies,
the ability to detect and locate a sudden change in
the variance in the time series is introduced. Using
this same procedure to detect a change in the long
memory parameter is also investigated. Applications
involve the Nile River minimum water levels and
vertical ocean shear measurements. In the
atmospheric sciences, broadband features in the
spectrum of recorded time series have been
hypothesized to be nonstationary events; e.g., the
Madden--Julian oscillation. The Madden--Julian
oscillation is a result of large-scale circulation
cells oriented in the equatorial plane from the
Indean Ocean to the central Pacific. The oscillation
has been noted to have higher frequencies during
warm events in El Nino--Southern Oscillation (ENSO)
years. The concepts of wavelet covariance and
wavelet correlation are introduced and applied to
this problem as an alternative to cross-spectrum
analysis. The wavelet covariance is shown to
decompose the covariance between two stationary
processes on a scale by scale basis. Asymptotic
normality of estimators of the wavelet covariance
and correlation is shown in order to construct
approximate confidence intervals. Both quantities
are generalized into the wavelet cross-covariance
and cross-correlation in order to investigate
possible lead/lag relations in bivariate time
series. Atmospheric measurements (such as station
pressure and zonal wind speeds) from a single
station at Canton Island (2.8S, 171.7W) are analyzed
and nicely replicate the results found in Madden and
Julian (1971). To highlight that the wavelet methods
can provide insight over and above traditional
spectral methods (including multitaper techniques) a
daily ``Southern Oscillation Index'' and station
pressure series from Truk Island (7.4N, 151.8W) are
analyzed. The wavelet cross-covariance nicely
decomposes the usual cross-covariance into scales
which are more easily associated with physical
phenomena. The time-varying wavelet covariance is
used to show the increase in positive correlation
between the SOI and Truk Island station pressure in
the first half of each year versus latter half.",
}
@Book{wic:adapted,
title = "Adapted Wavelet Analysis from Theory to Software",
author = "Mladen Victor Wickerhauser",
publisher = "A K Peters",
ISBN = "1-56881-041-5",
year = "1994",
address = "Wellesley, Massachusetts",
abstract = "This detail-oriented text is intended for engineers
and applied mathematicians who must write computer
programs to perform wavelet and related analyses on
real data. It should also be useful to the pure
mathematician with questions about wavelet theory
applications and to the instructor or student as a
textbook in the mathematics and latest techniques in
transient signal analysis and processing. Beginning
with an overview of mathematical prerequisites,
successive chapters rigorously examine the
properties of waveforms used in adapted wavelet
analysis: discrete ``fast'' Fourier transforms,
orthogonal and biorthogonal wavelets, wavelet
packets, and localized trigonometric or lapped
orthogonal functions. Other chapters discuss the
``best-basis'' method,time-frequency analysis, and
combinations of these algorithms useful for signal
analysis, de-noising, and data compression. Each
chapter discusses the technical aspects of
implementation giving examples in pseudocode backed
up with a Standard C source code (on optional
diskette) and closes with a list of worked
exercises.",
}
@Unpublished{wic:theory-applications,
title = "Wavelet Theory and Applications",
author = "Mladen Victor Wickerhauser",
year = "1997",
note = "Department of Mathematics, Washington University of
St. Louis",
}
@Unpublished{won-ip-lua-xie:detection,
title = "Wavelet Detection of Jump Points and an Application to
Exchange Rates",
author = "Heung Wong and Wai-Cheung Ip and Yihui Luan and
Zhongjie Xie",
year = "1996",
note = "The Hong Kong Polytechnic University, Hong Kong",
}
@Article{won:harmonizable,
title = "Wavelet decomposition of harmonizable random
processes",
author = "P. W. Wong",
journal = IEEETIT,
volume = "39",
number = "1",
year = "1993",
pages = "7--18",
keywords = "pointwise convergence, signal analysis, discrete
wavelet decomposition, second-order harmonizable
random processes, deterministic wavelet
decomposition, complex exponential, bounded
convergence, stochastic wavelet decomposition,
linear operations, addition, differentiation, linear
filtering",
abstract = "The discrete wavelet decomposition of second-order
harmonizable random processes is considered. The
deterministic wavelet decomposition of a complex
exponential function is examined, where its
pointwise and bounded convergence to the function is
proved. This result is then used for establishing
the stochastic wavelet decomposition of harmonizable
processes. The similarities and differences between
the wavelet decompositions of general harmonizable
processes and a subclass of processes having no
spectral mass at zero frequency, e.g., those that
are wide-sense stationary and have continuous power
spectral densities, are also investigated. The
relationships between the harmonization of a process
and that of its wavelet decomposition are
examined. Finally, certain linear operations such as
addition, differentiation, and linear filtering on
stochastic wavelet decompositions are considered. It
is shown that certain linear operations can be
performed term by term with the decomposition.",
}
@Article{wor-opp:self-similar,
title = "Wavelet-based representations for a class of
self-similar signals with application to fractal
modulation",
author = "Gregory W. Wornell and Alan V. Oppenheim",
journal = IEEETIT,
volume = "38",
number = "2",
year = "1992",
pages = "785--800",
keywords = "spectral characteristics, wavelet transforms,
self-similar signals, fractal modulation, deterministic
scale-invariance characterization, orthonormal wavelet
bases, dy-homogeneous signals, communications-based
context, multiple time-scales, multirate modulation
strategy, noisy channels",
abstract = "A potentially important family of self-similar signals
based upon a deterministic scale-invariance
characterization is introduced. These signals, which
are referred to as 'dy-homogeneous' signals because
they generalize the well-known homogeneous functions,
have highly convenient representations in terms of
orthonormal wavelet bases. In particular, wavelet
representations can be exploited to construct
orthonormal self-similar bases for these signals. The
spectral and fractal characteristics of dy-homogeneous
signals make them appealing candidates for use in a
number of applications. As one potential example, their
use in a communications-based context is considered.
Specifically, a strategy for embedding information into
a dy-homogeneous waveform on multiple time-scales is
developed. This multirate modulation strategy, called
fractal modulation, is potentially well-suited for use
with noisy channels of simultaneously unknown duration
and bandwidth.",
}
@Book{wor:book,
title = "Signal Processing with Fractals: {A} Wavelet Based
Approach",
author = "Gregory W. Wornell",
publisher = "Prentice Hall",
address = NJ,
year = "1996",
URL = "http://www.prenhall.com/books/ptr_013120999x.html",
keywords = "Wavelet Transformations, Statistically Self-Similar,
Detection and Estimation with Fractal Processes,
Deterministically Self-Similar Signals, Fractal
Modulation, Linear Self-Similar Systems",
abstract = "Fractal signals, derived from wavelet theory, are
ideally suited for use in many engineering
applications, ranging from communications to remote
sensing. This book provides an introduction to wavelet
theory from a signal processing perspective, and
details fractal signals and a collection of practical
wavelet-based techniques for representing and
manipulating fractal signals in various applications.",
}
@Article{wor:karhunen-loeve,
title = "A {K}arhunen-{L}o\'{e}ve-like expansion for $1/f$
processes via wavelets",
author = "Gregory W. Wornell",
journal = IEEETIT,
volume = "36",
number = "4",
year = "1990",
pages = "859--861",
keywords = "orthonormal wavelet bases, Karhunen-Loeve-like
expansion, 1/f processes, scaling processes,
uncorrelated random variables",
abstract = "While so-called 1/f or scaling processes emerge
regularly in modeling a wide range of natural
phenomena, as yet no entirely satisfactory framework
has been described for the analysis of such processes.
Orthonormal wavelet bases are used to provide a new
construction for nearly 1/f processes from a set of
uncorrelated random variables.",
}
@Article{wor:representations,
title = "Wavelet-based representations for the $1/f$ family of
fractal processes",
author = "G. W. Wornell",
journal = PIEEE,
volume = "81",
number = "10",
year = "1993",
pages = "1428--1450",
keywords = "signal detection, 1/f family, fractal processes,
orthonormal wavelet bases, frequency-domain
characterization, Karhunen-Loeve-type expansion,
estimation problems",
abstract = "It is demonstrated that 1/f fractal processes are, in
a broad sense, optimally represented in terms of
orthonormal wavelet bases. Specifically, via a useful
frequency-domain characterization for 1/f processes,
the wavelet expansion's role as a Karhunen-Loeve-type
expansion for 1/f processes is developed. As an
illustration of potential, it is shown that
wavelet-based representations naturally lead to highly
efficient solutions to some fundamental detection and
estimation problems involving 1/f processes.",
}
@InProceedings{wu-su:relationship,
title = "On the relationship between the self-similarities of
fractal signals and wavelet transforms",
author = "Bing-Fei Wu and Yu-Lin Su",
booktitle = "International Symposium on Signal Processing and its
Applications",
editor = "B. Boashash and N. Harle and A. A. Zoubir",
year = "1996",
pages = "736--739",
email = "bwu@haeshiuh.cn.nctu.edu.tw",
keywords = "fractal signals. wavelet transforms. stochastic
processes. correlation functions. power spectra.
fractal dimensions. probability measure function.
variance function. time series function. time-averaging
autocorrelation function. ensemble-averaging
autocorrelation function. time-averaging power
spectrum. average power spectrum. distribution
functions. stationary processes. nonstationary
processes. one-dimensional self-similarity. continuous
wavelet transform. discrete wavelet transform.
quadrature mirror filter structure. fractional Brownian
motion process",
abstract = "Since many natural phenomena are occasionally defined
as stochastic processes and the corresponding fractal
characteristics are hidden from their correlation
functions or power spectra, the topic would be of
interest in signal processing. In this paper, we
summarize the fractal dimensions and the relationship
of the fractal in probability measure, variance, time
series, time-averaging autocorrelation,
ensemble-averaging autocorrelation, time-averaging
power spectrum, average power spectrum and distribution
functions for stationary and nonstationary processes.
We also propose that the preservation of the
one-dimensional self-similarity of a fractal signal is
obtained by using the continuous wavelet transform
(CWT) and the discrete wavelet transform (DWT) with the
perfect reconstruction quadrature mirror filter
structure. Moreover, we extend the results to the
two-dimensional case and point out the relationship of
the self-similarities between the CWT and DWT of the
fractal signals. A fractional Brownian motion process
is provided as an example to show the results of this
paper.",
}
@Article{xia-ger-har-sut:design,
title = "Design of prefilters for discrete multiwavelet
transforms",
author = "Xiang-Gen Xia and Jeffrey S. Geronimo and Douglas P.
Hardin and Bruce W. Suter",
journal = IEEETSP,
volume = "44",
number = "1",
year = "1996",
pages = "25--35",
keywords = "discrete multiwavelet transforms pyramid algorithm
single wavelet transform coefficients tree-structured
multirate filter banks premultirate filter banks vector
filter banks discrete vector-valued wavelet transform
discrete-time vector-valued signals discrete
multiwavelet transform energy compaction.",
abstract = "The pyramid algorithm for computing single wavelet
transform coefficients is well known. The pyramid
algorithm can be implemented by using tree-structured
multirate filter banks. The authors propose a general
algorithm to compute multiwavelet transform
coefficients by adding proper premultirate filter banks
before the vector filter banks that generate
multiwavelets. The proposed algorithm can be thought of
as a discrete vector-valued wavelet transform for
certain discrete-time vector-valued signals. The
proposed algorithm can be also thought of as a discrete
multiwavelet transform for discrete-time signals. The
authors then present some numerical experiments to
illustrate the performance of the algorithm, which
indicates that the energy compaction for discrete
multiwavelet transforms may be better than the one for
conventional discrete wavelet transforms.",
}
@Article{xia-kuo-zha:optimal,
title = "{W}avelet coefficient computation with optimal
prefiltering",
journal = IEEETSP,
volume = "42",
number = "8",
year = "1994",
pages = "2191--7",
author = "Gen Xia Xiang and C. C. J. Kuo and Zhang Zhen",
abstract = "Discrete wavelet transform (DWT) is often used to
approximate wavelet series transform (WST) and
continuous wavelet transform (CWT), since it can be
computed numerically. In this research, we first study
the accuracy of the computed DWT coefficients obtained
from the Shensa (see ibid., vol.40, no.10, p.2464-2482,
1992) algorithm as an approximate of the WST
coefficients. Based on the accuracy analysis, we then
propose a procedure to design optimal FIR prefilters
used in the Shensa algorithm to reduce the
approximation error. Finally, numerical examples are
presented to demonstrate the performance of the optimal
FIR prefilters.",
keywords = "wavelet coefficient. optimal prefiltering. discrete
wavelet transform. DWT. wavelet series transform.
continuous wavelet transform. WST. CWT. accuracy
analysis. optimal FIR prefilters. approximation error
reduction. Shensa algorithm.",
}
@Article{yan-sag-tsu:system,
title = "System impulse response identification using a
multiresolution neural network",
author = "Zi-Jiang Yang and Setsuo Sagara and Teruo Tsuji",
journal = "Automatica",
volume = "33",
number = "7",
year = "1997",
pages = "1345--1350",
URL = "",
keywords = "system impulse response identification multiresolution
neural network discrete-time impulse response model
linear system sampled input-output data I/O data
high-frequency components continuous-time impulse
response scaling functions wavelet functions genetic
algorithm AIC redundant subsystems",
abstract = "This paper proposes a new identification method for
the discrete-time impulse response model of a linear
system from sampled input-output data. Our attention is
especially focused on identification of the impulse
response, which includes high-frequency components
locally. The continuous-time impulse response of the
system is approximated by a multiresolution neural
network composed of the scaling and wavelet functions.
Hence the system under study can be viewed as the
weighted sum of a group of subsystems in which the
scaling functions and wavelet functions are interpreted
as their impulse responses respectively. Then the
genetic algorithm and the AIC are introduced to select
significant subsystems at each resolution level such
that some redundant subsystems that are sensitive to
the noise effects are discarded. It is shown through a
simulation that the proposed method yields accurate
estimate of the impulse response, even in the
ill-conditioned cases.",
}
@Article{yu-mykland:looking,
title = "Looking at {M}arkov samplers through cusum path
plots: {A} simple diagnostic idea",
author = "Bin Yu and Per Mykland",
journal = SC,
volume = "8",
number = "3",
year = "1998",
pages = "275--286",
}
@Unpublished{zha:temporal-spatial,
title = "Multiresolution analysis for temporal-spatial
processes: {A} preliminary report",
author = "Jun Zhai",
year = "1997",
note = "Department of Statistics, North Carolina State
University",
}
@Article{zie-stu:relation,
title = "The relation of the {A}llan- and $\Delta$-variance
to the continuous wavelet transform",
author = "M. Zielinsky and J. Stutzki",
journal = AandA,
volume = "347",
number = "2",
year = "1999",
pages = "630--633",
URL = "http://xxx.lanl.gov/abs/astro-ph/9904190",
abstract = "This paper is understood as a supplement to the
paper by Stutzki et al. 1998, where we have shown
the usefulness of the Allan-variance and its higher
dimensional generalization, the Delta-variance, for
the characterization of molecular cloud
structures. In this study we present the connection
between the Allan- and Delta-variance and a more
popular structure analysis tool: the wavelet
transform. We show that the Allan- and
Delta-variances are the variances of wavelet
transform coefficients.",
}
@Book{fou-kum:geophysics,
title = "Wavelets in Geophysics",
booktitle = "Wavelets in Geophysics",
editor = "Efi Foufoula-Georgiou and Praveen Kumar",
series = "Wavelet Analysis and its Applications",
volume = "4",
publisher = "Academic Press, Inc",
year = "1994",
address = SD,
URL = "http://www.apcatalog.com/cgi-bin/AP?ISBN=0122628500&LOCATION=US&FORM=FORM2",
abstract = "Applications of wavelet analysis to the geophysical
sciences grew from Jean Morlet's work on seismic
signals in the 1980s. Used to detect signals against
noise, wavelet analysis excels for transients or for
spatially localized phenomena. In this fourth volume in
the renown WAVELET ANALYSIS AND ITS APPLICATIONS
Series, Efi Foufoula-Georgiou and Praveen Kumar begin
with a self-contained overview of the nature, power,
and scope of wavelet transforms. The eleven original
papers that follow in this edited treatise show how
geophysical researchers are using wavelets to analyze
such diverse phenomena as intermittent atmospheric
turbulence, seafloor bathymetry, marine and other
seismic data, and flow in aquifiers. Wavelets in
Geophysics will make informative reading for
geophysicists seeking an up-to-date account of how
these tools are being used as well as for wavelet
researchers searching for ideas for applications, or
even new points of departure.",
}
@Book{ant-opp:wavelets,
title = "Wavelets and Statistics",
booktitle = "Wavelets and Statistics",
editor = "Anestis Antoniadis and Georges Oppenheim",
series = "Lecture Notes in Statistics",
volume = "103",
year = "1995",
publisher = "Springer-Verlag",
address = NY,
ISBN = "0-387-94564-4",
URL = "http://www.springer-ny.com/catalog/np/aug95np/DATA/0-387-94564-4.html",
abstract = "Wavelets theory has found applications in a remarkable
diversity of disciplines. The volume presents the
proceedings of a conference held at Villard de Lans,
France in 1994. Both statistical results and practical
contributions were presented. The material is wide in
scope and ranges from the development of new tools for
nonparametric curve estimation to applied problems such
as detection of transients in signal processing and
image segmentation.",
}
@Proceedings{com-gro-tch:wavelets,
editor = "Jean-Michel Combes and Alexander Grossman and
Philippe Tchamitchian",
title = "Wavelets: Time-Frequency Methods and Phase Space",
booktitle = "Wavelets: Time-Frequency Methods and Phase Space",
series = "Inverse Problems and Theoretical Imaging",
publisher = "Springer-Verlag",
year = "1989",
address = "Berlin",
note = "Proceedings of the International Conference,
Marseille, France, December 14-18, 1987",
}
@Book{dag-ste:goodness,
title = "Goodness-of-Fit Techniques",
booktitle = "Goodness-of-Fit Techniques",
editor = "Ralph B. D'Agostino and Michael A. Stephens",
volume = "68",
series = "STATISTICS: Textbooks and Monographs",
publisher = "Marcel Dekker",
address = NY,
year = "1986",
pages = "560",
}
@Proceedings{lai-uns-ald:wavelet6,
title = "Wavelet applications in signal and image processing
{VI}",
booktitle = "Wavelet applications in signal and image processing
{VI}",
editor = "Andrew F. Laine and Michael A. Unser and Akram
Aldroubi",
volume = "3458",
year = "1998",
pages = "284",
series = "Proceedings of SPIE",
note = "19-24 July, 1998, San Diego, California",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/3400/3458.html",
}
@Proceedings{lai-uns:wavelet2,
title = "Wavelet applications in signal and image processing
{II}",
booktitle = "Wavelet applications in signal and image processing
{II}",
editor = "Andrew F. Laine and Michael A. Unser",
volume = "2303",
year = "1994",
pages = "602",
series = "Proceedings of SPIE",
note = "24-29 July, 1994, San Diego, California",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/2300/2303.html",
}
@Proceedings{lai-uns:wavelet3,
title = "Wavelet applications in signal and image processing
{III}",
booktitle = "Wavelet applications in signal and image processing
{III}",
editor = "Andrew F. Laine and Michael A. Unser and Mladen V.
Wickerhauser",
volume = "2569",
year = "1995",
pages = "900",
series = "Proceedings of SPIE",
note = "12-14 July, 1995, San Diego, California",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/2500/2569.html",
}
@Proceedings{lai:wavelet1,
title = "Mathematical Imaging: Wavelet Applications in Signal
and Image Processing",
booktitle = "Mathematical Imaging: Wavelet Applications in Signal
and Image Processing",
editor = "Andrew F. Laine",
volume = "2034",
series = "Proceedings of the SPIE",
year = "1993",
note = "11-16 July, 1993, San Diego, California",
URL = "http://www.spie.org/web/abstracts/2000/2034.html",
}
@Book{mul-vid:biwbm,
title = "Bayesian Inference in Wavelet-based Models",
booktitle = "Bayesian Inference in Wavelet-based Models",
editor = "Peter M{\"u}ller and Brani Vidakovic",
publisher = "Springer Verlag",
address = NY,
volume = "141",
series = "Lecture Notes in Statistics",
year = "1999",
pages = "",
}
@Book{rao-pri-les:applications,
title = "Applications of Time Series Analysis in Astronomy and
Meteorology",
booktitle = "Applications of Time Series Analysis in Astronomy and
Meteorology",
editor = "T. Subba Rao and M. B. Priestly and O. Lessi",
year = "1997",
publisher = "Chapman \& Hall",
address = "London",
ISBN = "0-412-63800-2",
abstract = "Statistical techniques, in particular time series
techniques, are widely used in astronomy and
meteorology. Despite this, until recently there have
been few attempts to bring researchers from the fields
of statistics, astronomy and meteorology together to
discuss and formalize important problems. Applications
of Time Series Analysis in Astronomy and Meteorology
brings together a series of papers by experts in these
fields evenly devoted to the theory and methodology of
time series and to its applications to astronomy,
meteorology and climatology. The topics covered include
detection of periodicities, spectral analysis of
unequally spaced data, detection of change points and
higher order spectral methods of non-linear and
non-Gaussian signals. Estimation of fractal dimension
and applications of wavelet methods to astronomy are
also considered. In addition, this book includes a
floppy disc containing data sets to serve as a
benchmark series. Applications of Time Series Analysis
in Astronomy and Meteorology is of interest to
statisticians, astronomers, meteorologists and
climatologists alike.",
}
@Book{sta-var:methods,
title = "Statistical Methods for Physical Science",
booktitle = "Statistical Methods for Physical Science",
editor = "John L. Stanford and Stephen B. Vardeman",
series = "Methods of Experimental Physics",
volume = "28",
year = "1994",
publisher = "Academic Press, Inc.",
address = "Boston",
keywords = "physical sciences, experiments, statistical methods",
}
@Proceedings{szu:wavelet1,
title = "Wavelet Applications",
booktitle = "Wavelet Applications",
editor = "Harold H. Szu",
volume = "2242",
year = "1994",
series = "Proceedings of SPIE",
pages = "994",
note = "4-8, April 1994, Orlando, Florida",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/2200/2242.html",
}
@Proceedings{szu:wavelet2,
title = "Wavelet Applications {II}",
booktitle = "Wavelet Applications {II}",
editor = "Harold H. Szu",
volume = "2491",
year = "1995",
series = "Proceedings of SPIE",
pages = "1183",
note = "17-21, April 1995, Orlando, Florida",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/2400/2491.html",
}
@Proceedings{szu:wavelet3,
title = "Wavelet Applications {III}",
booktitle = "Wavelet Applications {III}",
editor = "Harold H. Szu",
volume = "2762",
year = "1996",
series = "Proceedings of SPIE",
pages = "668",
note = "8-12 April 1996, Orlando, Florida",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/2700/2762.html",
}
@Proceedings{szu:wavelet5,
title = "Wavelet Applications {V}",
booktitle = "Wavelet Applications {V}",
editor = "Harold H. Szu",
volume = "3391",
year = "1998",
series = "Proceedings of SPIE",
pages = "",
note = "14-16 April 1998, Orlando, Florida",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/3300/3391.html",
}
@Proceedings{szu:wavelet6,
title = "Wavelet Applications {VI}",
booktitle = "Wavelet Applications {VI}",
editor = "Harold H. Szu",
volume = "3723",
year = "1999",
series = "Proceedings of SPIE",
pages = "478",
note = "4-9 April 1999, Orlando, Florida",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/3700/3723.html",
}
@Proceedings{uns-ald-lai:wavelet4,
title = "Wavelet Applications in Signal and Image Processing
{IV}",
booktitle = "Wavelet Applications in Signal and Image Processing
{IV}",
editor = "Michael A. Unser and Akram Aldroubi and Andrew F.
Laine",
volume = "2825",
year = "1996",
pages = "1044",
series = "Proceedings of SPIE",
note = "4-9 August, 1996, Denver, Colorado",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/2800/2825.html",
}
@Proceedings{uns-ald-lai:wavelet7,
title = "Wavelet Applications in Signal and Image Processing
{VII}",
booktitle = "Wavelet Applications in Signal and Image Processing
{VII}",
editor = "Michael A. Unser and Akram Aldroubi and Andrew F.
Laine",
volume = "3813",
year = "1999",
pages = "",
series = "Proceedings of SPIE",
note = "?-? October, 1996, Denver, Colorado",
keywords = "Image-processing, Signal-processing, Wavelets",
URL = "http://www.spie.org/web/abstracts/3800/3813.html",
}