{"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/on-the-strong-convexity-of-pnp-regularization","title":"On the Strong Convexity of PnP Regularization Using Linear Denoisers","arxiv_id":"2411.01027","date":"2024-11-01","proceeding":null,"authors":["Arghya Sinha","Kunal N Chaudhury"],"abstract":"In the Plug-and-Play (PnP) method, a denoiser is used as a regularizer within classical proximal algorithms for image reconstruction. It is known that a broad class of linear denoisers can be expressed as the proximal operator of a convex regularizer. Consequently, the associated PnP algorithm can be linked to a convex optimization problem $\\mathcal{P}$. For such a linear denoiser, we prove that $\\mathcal{P}$ exhibits strong convexity for linear inverse problems. Specifically, we show that the strong convexity of $\\mathcal{P}$ can be used to certify objective and iterative convergence of any PnP algorithm derived from classical proximal methods.","url_abs":"https://arxiv.org/abs/2411.01027v1","url_pdf":"https://arxiv.org/pdf/2411.01027v1.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":"on-the-strong-convexity-of-pnp-regularization","repo_url":"https://github.com/arghyasinha/PnP-StrongConvexity","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}