Image restoration using a stochastic variant of the alternating direction method of multipliers

Abstract

We propose an efficient image restoration framework based on stochastic optimization. Image restoration usually requires some iterative methods for solving optimization problems that characterize restored images, where the multiplication of the observation matrix Φ ϵ Rm × n and variables has to be computed at each iteration. If an efficient implementation of the multiplication (e.g., using FFT) is unavailable, its computational cost becomes O(MN), which is quite expensive since both N and M are usually large in image restoration. Our method needs to load and apply only a part of the observation matrix of size M/b × N (b: the number of parts), so that the computational cost is only O(MN/b). Moreover, the proposed method accepts various nonsmooth objectives effective for image restoration. Experiments on compressed sensing reconstruction and non-uniform deblurring show the advantage of the proposed method over state-of-the-art proximal optimization methods.