(A) study on the domain decomposition methods for the total variation minimization

Abstract

We propose nonoverlapping domain decomposition methods for solving total variation minimization problem. We decompose the domain of the dual problem into nonoverlapping rectangular subdomains, in which the local total variation problems are solved. We change the local dual problems into the equivalent primal form which reproduces the original problem at small dimension. Sequential and parallel algorithms are presented. The convergence of both algorithms is analyzed and numerical results are presented.