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A hierarchical Bayesian model for frame representation

Lotfi Chaâri 1, 2 Jean-Christophe Pesquet 3 Jean-Yves Tourneret 4, 2 Philippe Ciuciu 5 Amel Benazza-Benyahia 6
1 IRIT-TCI - Traitement et Compréhension d’Images
IRIT - Institut de recherche en informatique de Toulouse
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 LIGM - Laboratoire d'Informatique Gaspard-Monge
4 IRIT-SC - Signal et Communications
IRIT - Institut de recherche en informatique de Toulouse
5 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data
Inria Saclay - Ile de France, NEUROSPIN - Service NEUROSPIN
6 URISA - unité de Recherche en Imagerie Satellitaire et ses Applications
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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Conference papers
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https://hal-upec-upem.archives-ouvertes.fr/hal-00853350
Contributor : Jean-Christophe Pesquet Connect in order to contact the contributor
Submitted on : Thursday, August 22, 2013 - 2:39:58 PM
Last modification on : Saturday, January 15, 2022 - 3:57:37 AM

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  • HAL Id : hal-00853350, version 1

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CNRS | INRIA | UNIV-TLSE2 | PARISTECH | LIGM_SIGNAL | UNIV-MLV | UPEC-UPEM | ENPC | LIGM | CEA | CEA-DRF | JOLIOT | NEUROSPIN | UNIV-TLSE3 | UT1-CAPITOLE | IRIT | IRIT-SC | IRIT-TCI | IRIT-SI | IRIT-INPT

Citation

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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