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Bayesian anti-sparse coding

Elvira, Clément and Chainais, Pierre and Dobigeon, Nicolas Bayesian anti-sparse coding. (2017) IEEE Transactions on Signal Processing, 65 (7). 1660-1672. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2016.2645543

Abstract

Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients exhibits relevant properties in various applications such as digital communications. Anti-sparse regularization can be naturally expressed through an ℓ∞-norm penalty. This paper derives a probabilistic formulation of such representations. A new probability distribution, referred to as the democratic prior, is first introduced. Its main properties as well as three random variate generators for this distribution are derived. Then this probability distribution is used as a prior to promote anti-sparsity in a Gaussian linear inverse problem, yielding a fully Bayesian formulation of anti-sparse coding. Two Markov chain Monte Carlo (MCMC) algorithms are proposed to generate samples according to the posterior distribution. The first one is a standard Gibbs sampler. The second one uses Metropolis-Hastings moves that exploit the proximity mapping of the log-posterior distribution. These samples are used to approximate maximum a posteriori and minimum mean square error estimators of both parameters and hyperparameters. Simulations on synthetic data illustrate the performances of the two proposed samplers, for both complete and over-complete dictionaries. All results are compared to the recent deterministic variational FITRA algorithm.

Item Type:Article
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org The original PDF can be found at IEEE Transactions on Signal Processing (ISSN 1053-587X) website: http://ieeexplore.ieee.org/document/7801149/ Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, 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 component of this work in other works.
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Ecole Centrale de Lille (FRANCE)
Other partners > Université Lille 1, Sciences et Technologies - Lille 1 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:15 Feb 2018 12:44

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