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Split-and-augmented Gibbs sampler - Application to large scale inverse problems

Vono, Maxime and Dobigeon, Nicolas and Chainais, Pierre Split-and-augmented Gibbs sampler - Application to large scale inverse problems. (2019) IEEE Transactions on Signal Processing, 67 (6). 1648-1661. ISSN 1053-587X

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Official URL: https://doi.org/10.1109/TSP.2019.2894825

Abstract

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variablesplitting and data augmentation. In particular, the formulation of one of the proposed approaches isclosely related to the alternating direction method of multipliers (ADMM) main steps. The proposedframework enables to derive faster and more efficient sampling schemes than the current state-of-the-art methods and can embed the latter. By sampling efficiently the parameter to infer as well as thehyperparameters of the problem, the generated samples can be used to approximate Bayesian estimatorsof the parameters to infer. Additionally, the proposed approach brings confidence intervals at a lowcost contrary to optimization methods. Simulations on two often-studied signal processing problemsillustrate the performance of the two proposed samplers. All results are compared to those obtained byrecent state-of-the-art optimization and MCMC algorithms used to solve these problems.

Item Type:Article
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 - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (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 de Lille (FRANCE)
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Deposited On:05 Mar 2020 13:58

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