Plug-and-Play Algorithm Convergence Analysis From The Standpoint of Stochastic Differential Equation

• URL: http://arxiv.org/abs/2404.13866v1
• Date: Mon, 22 Apr 2024 04:31:09 GMT
• Title: Plug-and-Play Algorithm Convergence Analysis From The Standpoint of Stochastic Differential Equation
• Authors: Zhongqi Wang, Bingnan Wang, Maosheng Xiang,
• Abstract summary: We show that Lipschitz denoiser withschitz measurement function would be enough for its guarantee, instead previous Lipschitz denoiser condition.
• Score: 3.7550827441501844
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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