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Proximal Splitting Derivatives for Risk Estimation

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDELEDALLE, Charles
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorVAITER, Samuel
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPEYRÉ, Gabriel
hal.structure.identifierEquipe Image - Laboratoire GREYC - UMR6072
dc.contributor.authorFADILI, Jalal M.
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDOSSAL, Charles
dc.date.accessioned2024-04-04T02:25:26Z
dc.date.available2024-04-04T02:25:26Z
dc.date.created2012-02-14
dc.date.issued2012-04
dc.date.conference2012-04
dc.identifier.issn1742-6596
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189886
dc.description.abstractEnThis paper develops a novel framework to compute a projected Generalized Stein Unbiased Risk Estimator (GSURE) for a wide class of sparsely regularized solutions of inverse problems. This class includes arbitrary convex data fidelities with both analysis and synthesis mixed L1-L2 norms. The GSURE necessitates to compute the (weak) derivative of a solution w.r.t.~the observations. However, as the solution is not available in analytical form but rather through iterative schemes such as proximal splitting, we propose to iteratively compute the GSURE by differentiating the sequence of iterates. This provides us with a sequence of differential mappings, which, hopefully, converge to the desired derivative and allows to compute the GSURE. We illustrate this approach on total variation regularization with Gaussian noise and to sparse regularization with poisson noise, to automatically select the regularization parameter.
dc.description.sponsorshipAdaptivité pour la représentation des images naturelles et des textures - ANR-08-EMER-0009
dc.language.isoen
dc.publisherIOP Science
dc.source.titleProc. 2nd Int. Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
dc.title.enProximal Splitting Derivatives for Risk Estimation
dc.typeCommunication dans un congrès
dc.identifier.doi10.1088/1742-6596/386/1/012003
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.subject.halSciences de l'ingénieur [physics]/Traitement du signal et de l'image
dc.description.sponsorshipEuropeERC SIGMA-Vision
bordeaux.journalJournal of Physics: Conference Series
bordeaux.page012003
bordeaux.volume386
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleNCMIP'12
bordeaux.countryFR
bordeaux.title.proceedingProc. 2nd Int. Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
bordeaux.peerReviewedoui
hal.identifierhal-00670213
hal.version1
hal.invitednon
hal.proceedingsoui
hal.popularnon
hal.audienceInternationale
dc.subject.itSparsity
dc.subject.itregularization
dc.subject.itinverse problems
dc.subject.itrisk estimator
dc.subject.itGSURE
dc.subject.itautomatic differentiation
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00670213v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Proc.%202nd%20Int.%20Workshop%20on%20New%20Computational%20Methods%20for%20Inverse%20Problems%20(NCMIP%202012)&rft.jtitle=Journal%20of%20Physics:%20Conference%20Series&rft.date=2012-04&rft.volume=386&rft.spage=012003&rft.epage=012003&rft.eissn=1742-6596&rft.issn=1742-6596&rft.au=DELEDALLE,%20Charles&VAITER,%20Samuel&PEYR%C3%89,%20Gabriel&FADILI,%20Jalal%20M.&DOSSAL,%20Charles&rft.genre=unknown


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