Two variants of alternating direction method of multipliers without certain inner iterations and their application to image super-resolution

We propose 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 iterations of ADMM itself consists of solving a certain convex optimization problem which often requires the use of some iterative solver. Such inner iterations cause slow convergence. Our proposed algorithms avoid some of inner iterations by employing simplified updates. An efficacy of the proposed algorithm is shown in an image super-resolution problem. In this application, the resultant algorithm does not require matrix inversion which causes inner iterations of the original ADMM. A numerical example in the image super-resolution setting demonstrates that our proposed algorithms reduce CPU time to about 70-80 percent of the original ADMM.