An adaptive fixed-point proximity algorithm for solving total variation denoising models

We study an adaptive fixed-point proximity algorithm to solve the total variation denoising model. The objective function is a sum of two convex functions and one of them is composed by an affine transformation, which is usually a regularization term. By decoupling and splitting, the problem is changed into two subproblems. Due to the nonsmooth and nondifferentiability of the subproblem, we solve its proximity minimization problem instead of the original one. To overcome the “staircase” effect during the process of denoising, an adaptive criterion on proximity parameters is put forward. At last we apply the improved algorithm to solve the isotropic total variation denoising model. The numerical results are given to illustrate the efficiency of the algorithm.