A hierarchical Bayesian model for frame representation

Abstract : In many signal processing problems, it may be fruitful to represent the signal under study in a redundant linear decomposition called a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general, the frame synthesis operator is not bijective and consequently, the frame coefficients are not directly observable. In this work, a hierarchical Bayesian model is introduced to solve this problem. A hybrid MCMC algorithm is subsequently proposed to sample from the derived posterior distribution. We show that through classical Bayesian estimators, this algorithm allows us to determine these hyper-parameters, as well as the frame coefficients in applications to image denoising with uniform noise.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00853350
Contributor : Jean-Christophe Pesquet <>
Submitted on : Thursday, August 22, 2013 - 2:39:58 PM
Last modification on : Thursday, October 24, 2019 - 2:44:06 PM

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  • HAL Id : hal-00853350, version 1

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Lotfi Chaâri, Jean-Christophe Pesquet, Jean-Yves Tourneret, Philippe Ciuciu, Amel Benazza-Benyahia. A hierarchical Bayesian model for frame representation. IEEE International Conference Acoustics, Speech, and Signal (ICASSP), Mar 2010, Dallas, USA, France. pp.4086-4089. ⟨hal-00853350⟩

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