Three variants of alternating direction method of multipliers without certain inner iterations and their application to image super-resolution via sparse representation

摘要

We propose three variants of Alternating Direction Method of Multipliers (ADMM) employing simplified updates under additional assumptions. ADMM iteratively solves the minimization of the sum of two nonsmooth convex functions. Each iteration of ADMM itself consists of solving a certain convex optimization problem which often requires the use of some iterative solver. These inner iterations cause slow convergence. Our proposed algorithms avoid certain inner iterations by employing simplified updates. Indeed, in several scenarios of image super-resolution via sparse representation, the proposed algorithms do not require matrix inversion which causes inner iterations in the standard ADMM. Numerical examples for the image super-resolution setting demonstrate that our proposed algorithms reduce CPU time to about 21-77 percent of the standard ADMM.