Convergence of Nonconvex PnP-ADMM with MMSE Denoisers

• URL: http://arxiv.org/abs/2311.18810v1
• Date: Thu, 30 Nov 2023 18:52:47 GMT
• Title: Convergence of Nonconvex PnP-ADMM with MMSE Denoisers
• Authors: Chicago Park, Shirin Shoushtari, Weijie Gan, Ulugbek S. Kamilov
• Abstract summary: Plug-and-Play Alternating Direction Method of Multipliers (ADMM) is widely-used for physical measurement problems. It has however been observed that. ADMM often empirically converges even for expansive CNNs.
• Score: 8.034511587847158
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Plug-and-Play Alternating Direction Method of Multipliers (PnP-ADMM) is a widely-used algorithm for solving inverse problems by integrating physical measurement models and convolutional neural network (CNN) priors. PnP-ADMM has been theoretically proven to converge for convex data-fidelity terms and nonexpansive CNNs. It has however been observed that PnP-ADMM often empirically converges even for expansive CNNs. This paper presents a theoretical explanation for the observed stability of PnP-ADMM based on the interpretation of the CNN prior as a minimum mean-squared error (MMSE) denoiser. Our explanation parallels a similar argument recently made for the iterative shrinkage/thresholding algorithm variant of PnP (PnP-ISTA) and relies on the connection between MMSE denoisers and proximal operators. We also numerically evaluate the performance gap between PnP-ADMM using a nonexpansive DnCNN denoiser and expansive DRUNet denoiser, thus motivating the use of expansive CNNs.

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