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Bayesian selection for the l2-Potts model regularization parameter: 1D piecewise constant signal denoising

Frecon, Jordan and Pustelnik, Nelly and Dobigeon, Nicolas and Wendt, Herwig and Abry, Patrice Bayesian selection for the l2-Potts model regularization parameter: 1D piecewise constant signal denoising. (2017) IEEE Transactions on Signal Processing, 65 (19). 5215-5224. ISSN 1053-587X

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Official URL: https://ieeexplore.ieee.org/document/7946262/

Abstract

Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whose automated selection remains an involved and challenging problem. Conversely, fully Bayesian formalisms encapsulate the regularization parameter selection into hierarchical models, at the price of high computational costs. This contribution proposes an operational strategy that combines hierarchical Bayesian and Potts model formulations, with the double aim of automatically tuning the regularization parameter and of maintaining computational effciency. The proposed procedure relies on formally connecting a Bayesian framework to a l2-Potts functional. Behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively, and shown to compare favorably against those of a fully Bayesian hierarchical procedure, both in accuracy and in computational load.

Item Type:Article
Additional Information:Thanks to the IEEE (Institute of Electrical and Electronics Engineers). This paper is available at : https://ieeexplore.ieee.org/document/7946262/ “© 2018 IEEE. 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.
HAL Id:hal-01887965
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Normale Supérieure de Lyon - ENS de Lyon (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 > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Université de Lyon - UDL (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:11 Sep 2018 13:14

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