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Convergent plug-and-play with proximal denoiser and unconstrained regularization parameter

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHURAULT, Samuel
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierMéthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales [MOKAPLAN]
dc.contributor.authorCHAMBOLLE, Antonin
hal.structure.identifierImage, Modélisation, Analyse, GEométrie, Synthèse [IMAGES]
hal.structure.identifierDépartement Images, Données, Signal [IDS]
dc.contributor.authorLECLAIRE, Arthur
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
dc.date.accessioned2024-04-04T02:32:48Z
dc.date.available2024-04-04T02:32:48Z
dc.date.issued2023-11-02
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190417
dc.description.abstractEnIn this work, we present new proofs of convergence for Plug-and-Play (PnP) algorithms. PnP methods are efficient iterative algorithms for solving image inverse problems where regularization is performed by plugging a pre-trained denoiser in a proximal algorithm, such as Proximal Gradient Descent (PGD) or Douglas-Rachford Splitting (DRS). Recent research has explored convergence by incorporating a denoiser that writes exactly as a proximal operator. However, the corresponding PnP algorithm has then to be run with stepsize equal to $1$. The stepsize condition for nonconvex convergence of the proximal algorithm in use then translates to restrictive conditions on the regularization parameter of the inverse problem. This can severely degrade the restoration capacity of the algorithm. In this paper, we present two remedies for this limitation. First, we provide a novel convergence proof for PnP-DRS that does not impose any restrictions on the regularization parameter. Second, we examine a relaxed version of the PGD algorithm that converges across a broader range of regularization parameters. Our experimental study, conducted on deblurring and super-resolution experiments, demonstrate that both of these solutions enhance the accuracy of image restoration.
dc.description.sponsorshipRepenser la post-production d'archives avec des méthodes à patch, variationnelles et par apprentissage - ANR-19-CE23-0027
dc.description.sponsorshipModels, Inference and Synthesis for Texture In Color - ANR-19-CE40-0005
dc.language.isoen
dc.subject.enNonconvex optimization
dc.subject.enInverse problems
dc.subject.enPlug-and-play
dc.title.enConvergent plug-and-play with proximal denoiser and unconstrained regularization parameter
dc.typeDocument de travail - Pré-publication
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.subject.halInformatique [cs]/Intelligence artificielle [cs.AI]
dc.subject.halMathématiques [math]/Statistiques [math.ST]
dc.identifier.arxiv2311.01216
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04269033
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04269033v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-11-02&rft.au=HURAULT,%20Samuel&CHAMBOLLE,%20Antonin&LECLAIRE,%20Arthur&PAPADAKIS,%20Nicolas&rft.genre=preprint


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