A parallel primal-dual splitting method for image restoration

We develop a parallel primal-dual splitting method to solve large-scale image restoration problems, which involve the sum of several linear-operator-coupled nonsmooth but proximable terms. With the proposed method, the objective function is decomposed into pieces that can be processed individually. No inverse operator is involved in our method and the highly parallel structure makes it preferable in distributed computation. The convergence is proven and the convergence rate is analyzed. Besides, its equivalence to the relaxed parallel linearized alternating direction method of multipliers (PLADMM) is addressed. Applications to image restoration problems with compound l1-regularizer and comparisons with state-of-the-art methods are detailed to show the superiority of the proposed method.