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A Hierarchical Bayesian Model for Frame Representation

Chaari, Lotfi and Pesquet, Jean-Christophe and Tourneret, Jean-Yves and Ciuciu, Philippe and Benazza-Benyahia, Amel A Hierarchical Bayesian Model for Frame Representation. (2010) IEEE Transactions on Signal Processing, vol. 58 (n° 11). pp. 5560-5571. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2010.2055562

Abstract

In many signal processing problems, it is fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyperparameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the frame synthesis operator is not bijective. Consequently, the frame coefficients are not directly observable. This paper introduces a hierarchical Bayesian model for frame representation. The posterior distribution of the frame coefficients and model hyperparameters is derived. Hybrid Markov chain Monte Carlo algorithms are subsequently proposed to sample from this posterior distribution. The generated samples are then exploited to estimate the hyperparameters and the frame coefficients of the target signal. Validation experiments show that the proposed algorithms provide an accurate estimation of the frame coefficients and hyperparameters. Application to practical problems of image denoising in the presence of uniform noise illustrates the impact of the resulting Bayesian estimation on the recovered signal quality.

Item Type:Article
Additional Information:Thanks to Institute of Electrical and Electronics Engineers (IEEE)editor. The definitive version is available at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78. "(c) 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works."
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Commissariat à l'Energie Atomique et aux énergies alternatives - CEA
French research institutions > Centre National de la Recherche Scientifique - CNRS
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS
Université de Toulouse > Université de Toulouse II-Le Mirail - UTM
Université de Toulouse > Université de Toulouse I-Sciences Sociales - UT1
Other partners > Université du 7 Novembre à Carthage (TUNISIA)
Other partners > Université Paris-Est Marne-La-Vallée - UPEMLV (FRANCE)
Laboratory name:
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Deposited By: Jean-yves TOURNERET
Deposited On:17 Nov 2010 10:47

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