Plug-and-Play Algorithm Convergence Analysis From The Standpoint of Stochastic Differential Equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911848248377344 |
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| author | Wang, Zhongqi Wang, Bingnan Xiang, Maosheng |
| author_facet | Wang, Zhongqi Wang, Bingnan Xiang, Maosheng |
| contents | The Plug-and-Play (PnP) algorithm is popular for inverse image problem-solving. However, this algorithm lacks theoretical analysis of its convergence with more advanced plug-in denoisers. We demonstrate that discrete PnP iteration can be described by a continuous stochastic differential equation (SDE). We can also achieve this transformation through Markov process formulation of PnP. Then, we can take a higher standpoint of PnP algorithms from stochastic differential equations, and give a unified framework for the convergence property of PnP according to the solvability condition of its corresponding SDE. We reveal that a much weaker condition, bounded denoiser with Lipschitz continuous measurement function would be enough for its convergence guarantee, instead of previous Lipschitz continuous denoiser condition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_13866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Plug-and-Play Algorithm Convergence Analysis From The Standpoint of Stochastic Differential Equation Wang, Zhongqi Wang, Bingnan Xiang, Maosheng Computer Vision and Pattern Recognition Probability The Plug-and-Play (PnP) algorithm is popular for inverse image problem-solving. However, this algorithm lacks theoretical analysis of its convergence with more advanced plug-in denoisers. We demonstrate that discrete PnP iteration can be described by a continuous stochastic differential equation (SDE). We can also achieve this transformation through Markov process formulation of PnP. Then, we can take a higher standpoint of PnP algorithms from stochastic differential equations, and give a unified framework for the convergence property of PnP according to the solvability condition of its corresponding SDE. We reveal that a much weaker condition, bounded denoiser with Lipschitz continuous measurement function would be enough for its convergence guarantee, instead of previous Lipschitz continuous denoiser condition. |
| title | Plug-and-Play Algorithm Convergence Analysis From The Standpoint of Stochastic Differential Equation |
| topic | Computer Vision and Pattern Recognition Probability |
| url | https://arxiv.org/abs/2404.13866 |