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\title{A MINIMAX ENTROPY METHOD FOR BLIND SEPARATION OF DEPENDENT COMPONENTS
IN ASTROPHYSICAL IMAGES}
\author{Cesar F. Caiafa$^{1}$, \underline{Ercan E. Kuruo\u{g}lu}$^{2}$ and
Araceli N. Proto$^{1,3}$ \\
%EndAName
{\small (1) Lab. de Sistemas Complejos. Fac. de Ingenier\'{\i}a (UBA),
Buenos Aires, Argentina}\\
{\small (2) Istituto di Scienza e Tecnologie dell'Informazione - CNR, Pisa,
Italy}\\
{\small (3) Comisi\'{o}n de Inv. Cient\'{\i}ficas de la Prov. de Buenos
Aires, Buenos Aires, Argentina}\\
{\small \ (e-mail: ccaiafa@fi.uba.ar, ercan.kuruoglu@isti.cnr.it and
aproto@fi.uba.ar) }}
\date{}
\maketitle

\begin{abstract}
\noindent We develop a new technique for the blind separation of potentially
non independent components in astrophysical images. Given a set of linearly
mixed images, corresponding to different measurement channels, we estimate
the original electromagnetic radiation sources in a blind fashion.
Specifically, we investigate the separation of cosmic microwave background
(CMB), thermal dust and galactic synchrotron emissions without imposing any
assumption on the mixing matrix. In our approach, we use the Gaussian and
non-Gaussian features of astrophysical sources and we assume that CMB-dust
and CMB-synchrotron are uncorrelated pairs while dust and synchrotron are
correlated which is in agreement with theory. These assumptions allow us to
develop an algorithm which associates the Minimum Entropy solutions with the
non-Gaussian sources (thermal dust and galactic synchrotron emissions) and
the Maximum Entropy solution as the only Gaussian source which is the CMB.
This new method is more appropriate than ICA algorithms because independence
between sources is not imposed which is a more realistic situation. We
investigate several measures associated with entropy and we compare them.
Finally, we present an example of separation using the Euclidean distance
between the Gaussian probability density function (pdf) and a Parzen based
estimation of the pdf associated with the data. For the validation of our
approach we present experimental results using a database that simulates de
one expected from the instruments that will operate onboard ESA's \textit{%
Planck} Surveyor Satellite to measure the CMB anisotropies all over the
celestial sphere.

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\medskip \noindent {Key Words: } Entropy measures, Blind Source Separation
(BSS), astrophysical images.
\end{abstract}

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