{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/fista-iterates-converge-linearly-for-denoiser","title":"FISTA Iterates Converge Linearly for Denoiser-Driven Regularization","arxiv_id":"2411.10808","date":"2024-11-16","proceeding":null,"authors":["Arghya Sinha","Kunal N. Chaudhury"],"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.","url_abs":"https://arxiv.org/abs/2411.10808v1","url_pdf":"https://arxiv.org/pdf/2411.10808v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"fista-iterates-converge-linearly-for-denoiser","repo_url":"https://github.com/arghyasinha/PnP-FISTA","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}