dc.contributor.author Peyré, Gabriel dc.contributor.author Fadili, Jalal dc.contributor.author Raguet, Hugo dc.date.accessioned 2012-01-18T14:45:23Z dc.date.available 2012-01-18T14:45:23Z dc.date.issued 2013 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/7892 dc.language.iso en en dc.subject wavelets en dc.subject total variation en dc.subject image processing en dc.subject convex optimization en dc.subject proximal en dc.subject splitting en dc.subject Forward-backward algorithm en dc.subject.ddc 621.3 en dc.title A Generalized Forward-Backward Splitting en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Groupe 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.abstracten This 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.isversionofjnlname SIAM Journal on Imaging Sciences dc.relation.isversionofjnlvol 6 dc.relation.isversionofjnlissue 3 dc.relation.isversionofjnldate 2013 dc.relation.isversionofjnlpages 1199–1226 dc.relation.isversionofdoi http://dx.doi.org/10.1137/120872802 dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00613637 en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher SIAM dc.subject.ddclabel Traitement du signal en
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