Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective
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The Plug-and-Play (PnP) ADMM algorithm is a powerful image restoration framework that allows advanced image denoising priors to be integrated into physical forward models to yield a provably convergent algorithm. However, despite the enormous applications and promising results, very little is known about why the PnP ADMM performs so well. This paper presents a formal analysis of the performance of PnP ADMM. By restricting the denoisers to the class of graph filters, or more specifically the symmetric smoothing filters, we offer three contributions: (1) We rigorously show conditions under which an equivalent maximum-a-posteriori (MAP) optimization exists, (2) we derive the mean squared error of the PnP solution, and provide a simple geometric interpretation which can explain the performance, (3) we introduce a new analysis technique via the concept of consensus equilibrium, and provide interpretations to general linear inverse problems and problems with multiple priors.
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