A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoiser
Hurault, Samuel; Chambolle, Antonin; Leclaire, Arthur; Papadakis, Nicolas (2023), A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoiser. https://basepub.dauphine.psl.eu/handle/123456789/24490
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Type
Document de travail / Working paperDate
2023Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSLPublished in
Paris
Pages
21
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Hurault, SamuelInstitut de Mathématiques de Bordeaux [IMB]
Chambolle, Antonin

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Leclaire, Arthur
Institut de Mathématiques de Bordeaux [IMB]
Papadakis, Nicolas
Institut de Mathématiques de Bordeaux [IMB]
Abstract (EN)
This paper presents a new convergent Plug-and-Play (PnP) algorithm. PnP methods are efficient iterative algorithms for solving image inverse problems formulated as the minimization of the sum of a data-fidelity term and a regularization term. PnP methods perform regularization by plugging a pre-trained denoiser in a proximal algorithm, such as Proximal Gradient Descent (PGD). To ensure convergence of PnP schemes, many works study specific parametrizations of deep denoisers. However, existing results require either unverifiable or suboptimal hypotheses on the denoiser, or assume restrictive conditions on the parameters of the inverse problem. Observing that these limitations can be due to the proximal algorithm in use, we study a relaxed version of the PGD algorithm for minimizing the sum of a convex function and a weakly convex one. When plugged with a relaxed proximal denoiser, we show that the proposed PnP-α PGD algorithm converges for a wider range of regularization parameters, thus allowing more accurate image restoration.Related items
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