Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective
This provides theoretical insights for researchers in image processing and optimization, but it is incremental as it builds on existing PnP ADMM frameworks.
The paper tackled the lack of understanding of why Plug-and-Play ADMM performs well in image restoration by analyzing it from a graph signal processing perspective, showing conditions for MAP equivalence and attributing performance gains to an intrinsic pre-denoising characteristic.
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 generate high quality image restoration results. However, despite the enormous number of applications and several theoretical studies trying to prove the convergence by leveraging tools in convex analysis, very little is known about why the algorithm is doing so well. The goal of this paper is to fill the gap by discussing the performance of PnP ADMM. By restricting the denoisers to the class of graph filters under a linearity assumption, or more specifically the symmetric smoothing filters, we offer three contributions: (1) We show conditions under which an equivalent maximum-a-posteriori (MAP) optimization exists, (2) we present a geometric interpretation and show that the performance gain is due to an intrinsic pre-denoising characteristic of the PnP prior, (3) we introduce a new analysis technique via the concept of consensus equilibrium, and provide interpretations to problems involving multiple priors.