A Parallel Proximal Algorithm for Anisotropic Total Variation Minimization

Total variation (TV) is a one of the most popular regularizers for stabilizing the solution of ill-posed inverse problems. This paper proposes a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functionals. Unlike traditional methods that require nested iterations for computing the proximal step of TV, our algorithm approximates the latter with several simple proximals that have closed form solutions. We theoretically prove that the proposed parallel proximal method achieves the TV solution with arbitrarily high precision at a global rate of converge that is equivalent to the fast proximal-gradient methods. The results in this paper have the potential to enhance the applicability of TV for solving very large-scale imaging inverse problems.