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In plug-and-play image restoration, the regularization is performed usingpowerful denoisers such as nonlocal means (NLM) or BM3D. This is done withinthe framework of alternating direction method of multipliers (ADMM), where theregularization step is formally replaced by an off-the-shelf denoiser. Eachplug-and-play iteration involves the inversion of the forward model followed bya denoising step. In this paper, we present a couple of ideas for improving theefficiency of the inversion and denoising steps. First, we propose to uselinearized ADMM, which generally allows us to perform the inversion at a lowercost than standard ADMM. Moreover, we can easily incorporate hard constraintsinto the optimization framework as a result. Second, we develop a fastalgorithm for doubly stochastic NLM, originally proposed by Sreehari et al.(IEEE TCI, 2016), which is about 80x faster than brute-force computation. Thisparticular denoiser can be expressed as the proximal map of a convexregularizer and, as a consequence, we can guarantee convergence for linearizedplug-and-play ADMM. We demonstrate the effectiveness of our proposals forsuper-resolution and single-photon imaging.

Linearized ADMM and Fast Nonlocal Denoising for Efficient Plug-and-Play Restoration