Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration

Abstract : Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily smooth. Our framework can handle stochastic approximations of the gradient of the smooth function and allows for stochastic errors in the evaluation of the proximity operator of the nonsmooth function. The almost sure convergence of the iterates generated by the algorithm to a minimizer is established under relatively mild assumptions. We also propose a stochastic version of a popular primal-dual proximal splitting algorithm, establish its convergence, and apply it to an online image restoration problem.
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Communication dans un congrès
European Signal and Image Processing Conference (EUSIPCO 2016), Aug 2016, Budapest, Hungary. pp.1813 - 1817, 2016, <http://www.eusipco2016.org>. <10.1109/EUSIPCO.2016.7760561>
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Contributeur : Jean-Christophe Pesquet <>
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Dernière modification le : samedi 18 février 2017 - 01:14:50
Document(s) archivé(s) le : vendredi 24 mars 2017 - 12:21:24

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Patrick Combettes, Jean-Christophe Pesquet. Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration. European Signal and Image Processing Conference (EUSIPCO 2016), Aug 2016, Budapest, Hungary. pp.1813 - 1817, 2016, <http://www.eusipco2016.org>. <10.1109/EUSIPCO.2016.7760561>. <hal-01422154>

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