Alternating direction method of multiplier (ADMM) is a widely used algorithmfor solving constrained optimization problems in image restoration. Among manyuseful features, one critical feature of the ADMM algorithm is its modularstructure which allows one to plug in any off-the-shelf image denoisingalgorithm for a subproblem in the ADMM algorithm. Because of the plug-innature, 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 ofrecent papers. However, it is unclear under what conditions and by using whatdenoising algorithms would it guarantee convergence. Also, since Plug-and-PlayADMM uses a specific way to split the variables, it is unclear if fastimplementation can be made for common Gaussian and Poissonian image restorationproblems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixedpoint convergence. We show that for any denoising algorithm satisfying anasymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges toa fixed point under a continuation scheme. We also present fast implementationsfor two image restoration problems on super-resolution and single-photonimaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in eachproblem type, and demonstrate promising experimental results of the algorithm.
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