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dc.contributor.authorPeyré, Gabriel
dc.contributor.authorFadili, Jalal
dc.contributor.authorRaguet, Hugo
dc.date.accessioned2012-01-18T14:45:23Z
dc.date.available2012-01-18T14:45:23Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7892
dc.language.isoenen
dc.subjectwaveletsen
dc.subjecttotal variationen
dc.subjectimage processingen
dc.subjectconvex optimizationen
dc.subjectproximalen
dc.subjectsplittingen
dc.subjectForward-backward algorithmen
dc.subject.ddc621.3en
dc.titleA Generalized Forward-Backward Splittingen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherGroupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC) http://www.greyc.unicaen.fr/ CNRS : UMR6072 – Université de Caen – Ecole Nationale Supérieure d'Ingénieurs de Caen;France
dc.description.abstractenThis paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than $n = 1$ non-smooth function, our method generalizes it to the case of arbitrary $n$. Our method makes an explicit use of the regularity of $F$ in the forward step, and the proximity operators of the $G_i$'s are applied in parallel in the backward step. This allows the generalized forward backward to efficiently address an important class of convex problems. We prove its convergence in infinite dimension, and its robustness to errors on the computation of the proximity operators and of the gradient of $F$. Examples on inverse problems in imaging demonstrate the advantage of the proposed methods in comparison to other splitting algorithms.en
dc.relation.isversionofjnlnameSIAM Journal on Imaging Sciences
dc.relation.isversionofjnlvol6
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages1199–1226
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/120872802
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00613637en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSIAM
dc.subject.ddclabelTraitement du signalen


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