Dual-primal domain decomposition methods for the total variation minimization

Abstract

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