FISTA Iterates Converge Linearly for Denoiser-Driven Regularization

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Autori principali: Sinha, Arghya, Chaudhury, Kunal N.
Natura: Preprint
Pubblicazione: 2024
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author Sinha, Arghya
Chaudhury, Kunal N.
author_facet Sinha, Arghya
Chaudhury, Kunal N.
contents The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play ($\texttt{PnP}$) and Regularization-by-Denoising ($\texttt{RED}$). We consider two specific algorithms $\texttt{PnP-FISTA}$ and $\texttt{RED-APG}$, where regularization is performed by replacing the proximal operator in the $\texttt{FISTA}$ algorithm with a powerful denoiser. The iterate convergence of $\texttt{FISTA}$ is known to be challenging with no universal guarantees. Yet, we show that for linear inverse problems and a class of linear denoisers, global linear convergence of the iterates of $\texttt{PnP-FISTA}$ and $\texttt{RED-APG}$ can be established through simple spectral analysis.
format Preprint
id arxiv_https___arxiv_org_abs_2411_10808
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
Sinha, Arghya
Chaudhury, Kunal N.
Optimization and Control
Image and Video Processing
94A08, 41A25, 65F10
The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play ($\texttt{PnP}$) and Regularization-by-Denoising ($\texttt{RED}$). We consider two specific algorithms $\texttt{PnP-FISTA}$ and $\texttt{RED-APG}$, where regularization is performed by replacing the proximal operator in the $\texttt{FISTA}$ algorithm with a powerful denoiser. The iterate convergence of $\texttt{FISTA}$ is known to be challenging with no universal guarantees. Yet, we show that for linear inverse problems and a class of linear denoisers, global linear convergence of the iterates of $\texttt{PnP-FISTA}$ and $\texttt{RED-APG}$ can be established through simple spectral analysis.
title FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
topic Optimization and Control
Image and Video Processing
94A08, 41A25, 65F10
url https://arxiv.org/abs/2411.10808