International Conference on Mathematical Modeling in Industry 
<a href=" http://www.lcad.icmc.usp.br/icmmi/" target="_new">  
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ICMMI 2011, November 30-December 3, Sao Paolo, Bresil</a> 
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<a href="http://www.lcad.icmc.usp.br/icmmi/index.php/invited-speakers" target="_new">
Invited talk</a> 
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Title: 
Sparsity enforcing prior models and Bayesian approach for signal and image reconstruction

Abstract:
In this talk, we propose different prior modelling for signals and images
which can be used in a Bayesian inference approach in many inverse problems
in signal and image processing.
The sparsity may be directly on the original space or in a transformed space.
Here we consider it directly on the original space (impulsive signals).
Between the possible models, we focus on some of them which are either heavy tailed
(Generalized Gaussian, Student-t or Cauchy)
or mixture models (Mixture of Gaussians, Bernouilli-Gaussian, Bernouilli-Gamma,..).
Depending on the prior model selected, the Bayesian computations (optimization
for the Joint Maximum A Posteriori (MAP) estimate or MCMC or Variational Bayes
Approximations (VBA) for Posterior Means (PM) or complete density estimation)
may become more complex.
We propose these models, discuss on different possible Bayesian estimators,
describe the corresponding appropriate algorithms, and discuss on their corresponding
relative complexities and performances.
We show the results of the proposed methods on some applications such as
Signal deconvolution, Image restoration and Computed Tomography.