  In plug-and-play image restoration, the regularization is performed using
powerful denoisers such as nonlocal means (NLM) or BM3D. This is done within
the framework of alternating direction method of multipliers (ADMM), where the
regularization step is formally replaced by an off-the-shelf denoiser. Each
plug-and-play iteration involves the inversion of the forward model followed by
a denoising step. In this paper, we present a couple of ideas for improving the
efficiency of the inversion and denoising steps. First, we propose to use
linearized ADMM, which generally allows us to perform the inversion at a lower
cost than standard ADMM. Moreover, we can easily incorporate hard constraints
into the optimization framework as a result. Second, we develop a fast
algorithm for doubly stochastic NLM, originally proposed by Sreehari et al.
(IEEE TCI, 2016), which is about 80x faster than brute-force computation. This
particular denoiser can be expressed as the proximal map of a convex
regularizer and, as a consequence, we can guarantee convergence for linearized
plug-and-play ADMM. We demonstrate the effectiveness of our proposals for
super-resolution and single-photon imaging.
