A parallel alternating direction method with application to compound l1-regularized imaging inverse problems.

We derive a parallel alternating direction method of multipliers (PADMM) and apply it to compound l1-regularized imaging inverse problems. The proposed method is capable of locating the saddle point of large-scale convex minimization problems with the sum of several nonsmooth but proximable terms. Using an operator splitting strategy, the objective is decomposed into subproblems that are conveniently, individually and simultaneously solved. With the assistance of the Moreau decomposition, our method excludes auxiliary variables that exist in the ADMM and possesses a compacter structure. Thus, the proposed method is preferable in distributed computation. The convergence proof and convergence rate analysis are presented. Application to both image restoration and image compressed sensing demonstrates the effectiveness and efficiency of the proposed method.