FISTA Iterates Converge Linearly for Denoiser-Driven Regularization
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915023221161984 |
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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 |