Image Recovery by Combined Peaceman-Rachford and Douglas-Rachford Operator Splitting Method

Image recovery is a longstanding problems in many areas of image processing. In mathematics, the objective is often to minimize the sum of two (not necessarily smooth) lower semicontinuous convex functions in a real Hilbert space. A combined Peaceman-Rachford and Douglas-Rachford algorithm for monotone operator-splitting is proposed to solve this generic problem. The convergence of the method is obtained under general conditions. Applications to image deblurring and non-Gaussian denoising with a tight frame are also presented. Finally numerical computations comparing with other classical operator splitting methods are demonstrated.