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We consider the problem of finding the minimization of the sum of a convexfunction and the composition of another convex function with a continuouslinear operator from the view of fixed point algorithms based on proximityoperators. We design a primal-dual fixed point algorithm with dynamic stepsizebased on the proximity operator and obtain a scheme with a closed form solutionfor each iteration. Based on Modified Mann iteration and the firmlynonexpansive properties of the proximity operator, we achieve the convergenceof the proposed algorithm.

Efficient primal-dual fixed point algorithm with dynamic stepsize for convex problems with applications to imaging restoration