Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications

TL;DR

This paper introduces a convergent version of Plug-and-Play ADMM for image restoration, providing theoretical guarantees and demonstrating fast, effective applications in super-resolution and single-photon imaging.

Contribution

It establishes fixed point convergence conditions for Plug-and-Play ADMM with bounded denoisers and presents efficient implementations for specific image restoration tasks.

Findings

Converges to a fixed point under certain denoiser conditions

Achieves competitive results in super-resolution tasks

Performs well in single-photon imaging applications

Abstract

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name "Plug-and-Play ADMM". Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on super-resolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type, and demonstrate promising experimental results of the algorithm.