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arXiv · 2411.10808

FISTA Iterates Converge Linearly for Denoiser-Driven Regularization

Arghya Sinha·Kunal N. Chaudhury
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Abstract

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.

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Arghya Sinha, Kunal N. Chaudhury. 2024-11-16. FISTA Iterates Converge Linearly for Denoiser-Driven Regularization. https://arxiv.org/abs/2411.10808

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