HURAULT, Samuel; CHAMBOLLE, Antonin; LECLAIRE, Arthur; PAPADAKIS, Nicolas

Métadonnées

Licence d’utilisation du document

HURAULT, Samuel
Institut de Mathématiques de Bordeaux [IMB]

CHAMBOLLE, Antonin
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales [MOKAPLAN]

LECLAIRE, Arthur
Image, Modélisation, Analyse, GEométrie, Synthèse [IMAGES]
Département Images, Données, Signal [IDS]

Langue

Document de travail - Pré-publication

Ce document a été publié dans

2023-11-02

Résumé en anglais

In 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.< Réduire

Mots clés en anglais

Nonconvex optimization

Inverse problems

Plug-and-play

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190417

Project ANR

Repenser la post-production d'archives avec des méthodes à patch, variationnelles et par apprentissage - ANR-19-CE23-0027
Models, Inference and Synthesis for Texture In Color - ANR-19-CE40-0005

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251