On the Strong Convexity of PnP Regularization Using Linear Denoisers
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910681406636032 |
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| author | Sinha, Arghya Chaudhury, Kunal N |
| author_facet | Sinha, Arghya Chaudhury, Kunal N |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Strong Convexity of PnP Regularization Using Linear Denoisers Sinha, Arghya Chaudhury, Kunal N Optimization and Control Image and Video Processing 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. |
| title | On the Strong Convexity of PnP Regularization Using Linear Denoisers |
| topic | Optimization and Control Image and Video Processing |
| url | https://arxiv.org/abs/2411.01027 |