Linearized ADMM and Fast Nonlocal Denoising for Efficient Plug-and-Play Restoration
This work improves computational efficiency for image restoration tasks, though it is incremental as it builds on existing plug-and-play and denoising methods.
The paper tackled the efficiency of plug-and-play image restoration by proposing linearized ADMM to reduce inversion costs and a fast algorithm for doubly stochastic nonlocal means denoising, achieving about 80x speedup and demonstrating effectiveness in super-resolution and single-photon imaging.
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.