Linear Convergence of Plug-and-Play Algorithms with Kernel Denoisers
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918028799639552 |
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| author | Sinha, Arghya Kumar, Bhartendu Athalye, Chirayu D. Chaudhury, Kunal N. |
| author_facet | Sinha, Arghya Kumar, Bhartendu Athalye, Chirayu D. Chaudhury, Kunal N. |
| contents | The use of denoisers for image reconstruction has shown significant potential, especially for the Plug-and-Play (PnP) framework. In PnP, a powerful denoiser is used as an implicit regularizer in proximal algorithms such as ISTA and ADMM. The focus of this work is on the convergence of PnP iterates for linear inverse problems using kernel denoisers. It was shown in prior work that the update operator in standard PnP is contractive for symmetric kernel denoisers under appropriate conditions on the denoiser and the linear forward operator. Consequently, we could establish global linear convergence of the iterates using the contraction mapping theorem. In this work, we develop a unified framework to establish global linear convergence for symmetric and nonsymmetric kernel denoisers. Additionally, we derive quantitative bounds on the contraction factor (convergence rate) for inpainting, deblurring, and superresolution. We present numerical results to validate our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Convergence of Plug-and-Play Algorithms with Kernel Denoisers Sinha, Arghya Kumar, Bhartendu Athalye, Chirayu D. Chaudhury, Kunal N. Image and Video Processing Optimization and Control 94A08, 41A25, 65F10 The use of denoisers for image reconstruction has shown significant potential, especially for the Plug-and-Play (PnP) framework. In PnP, a powerful denoiser is used as an implicit regularizer in proximal algorithms such as ISTA and ADMM. The focus of this work is on the convergence of PnP iterates for linear inverse problems using kernel denoisers. It was shown in prior work that the update operator in standard PnP is contractive for symmetric kernel denoisers under appropriate conditions on the denoiser and the linear forward operator. Consequently, we could establish global linear convergence of the iterates using the contraction mapping theorem. In this work, we develop a unified framework to establish global linear convergence for symmetric and nonsymmetric kernel denoisers. Additionally, we derive quantitative bounds on the contraction factor (convergence rate) for inpainting, deblurring, and superresolution. We present numerical results to validate our theoretical findings. |
| title | Linear Convergence of Plug-and-Play Algorithms with Kernel Denoisers |
| topic | Image and Video Processing Optimization and Control 94A08, 41A25, 65F10 |
| url | https://arxiv.org/abs/2505.15318 |