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Solving an optimization problem whose objective function is the sum of twoconvex functions has received considerable interests in the context of imageprocessing recently. In particular, we are interested in the scenario when anon-differentiable convex function such as the total variation (TV) norm isincluded in the objective function due to many variational models establishedin image processing have this nature. In this paper, we propose a fast fixedpoint algorithm based on the quasi-Newton method for solving this class ofproblem, and apply it in the field of TV-based image deblurring. The novelmethod is derived from the idea of the quasi-Newton method, and the fixed-pointalgorithms based on the proximity operator, which were widely investigated veryrecently. Utilizing the non-expansion property of the proximity operator wefurther investigate the global convergence of the proposed algorithm. Numericalexperiments on image deblurring problem with additive or multiplicative noiseare presented to demonstrate that the proposed algorithm is superior to therecently developed fixed-point algorithm in the computational efficiency.

Fixed Point Algorithm Based on Quasi-Newton Method for Convex Minimization Problem with Application to Image Deblurring