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dc.contributor.authorVaiter, Samuel*
dc.contributor.authorGolbabaee, Mohammad*
dc.contributor.authorFadili, Jalal*
dc.contributor.authorPeyré, Gabriel*
dc.date.accessioned2014-07-21T08:40:26Z
dc.date.available2014-07-21T08:40:26Z
dc.date.issued2015
dc.identifier.issn2049-8764
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13750
dc.language.isoenen
dc.subjectSparsity
dc.subjectPartial smoothness
dc.subjectInverse problems
dc.subjectCompressed Sensing
dc.subjectonvex regularization
dc.subjectModel selection
dc.subjectTotal variation
dc.subject.ddc519en
dc.titleModel Selection with Low Complexity Priors
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherGroupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC) http://www.greyc.fr;France
dc.description.abstractenRegularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied regularization models with various types of low-dimensional structures. In such settings, the general approach is to solve a regularized optimization problem, which combines a data fidelity term and some regularization penalty that promotes the assumed low-dimensional/simple structure. This paper provides a general framework to capture this low-dimensional structure through what we coin partly smooth functions relative to a linear manifold. These are convex, non-negative, closed and finite-valued functions that will promote objects living on low-dimensional subspaces. This class of regularizers encompasses many popular examples such as the L1 norm, L1-L2 norm (group sparsity), as well as several others including the Linfty norm. We also show that the set of partly smooth functions relative to a linear manifold is closed under addition and pre-composition by a linear operator, which allows to cover mixed regularization, and the so-called analysis-type priors (e.g. total variation, fused Lasso, finite-valued polyhedral gauges). Our main result presents a unified sharp analysis of exact and robust recovery of the low-dimensional subspace model associated to the object to recover from partial measurements. This analysis is illustrated on a number of special and previously studied cases, and on an analysis of the performance of Linfty regularization in a compressed sensing scenario.
dc.relation.isversionofjnlnameInformation and Inference
dc.relation.isversionofjnlvol4
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages230-287
dc.relation.isversionofdoi10.1093/imaiai/iav005
dc.identifier.urlsitehttps://arxiv.org/abs/1307.2342v2
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingprintoui
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-04-19T14:25:12Z
hal.person.labIds*
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hal.person.labIds60*
hal.person.labIds60*


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