A Nonconvex Model With MCP For Image Restoration

In this paper,we introduce a nonconvex model for image processing with a minimax concave penalty.In general,we know that a natural image is mostly sparse under some transformation.So in the sense of compressed sensing,it amounts to minimizing the L0 norm.Traditionally,it is popular to use L1 penalty to bypass the NP hard L0 problem.However,recent studies show that nonconvex penalties have better performance when it comes to approach L0 norm.Thus we consider to adopt a nonconvex penalty function to construct a model for image processing.In this paper,we have proved the existence of a global minimizer for our nonconvex model.Then by using the alternating direction method of multipliers(ADMM)algorithm,we are able to solve our model.Moreover,under some suitable assumptions,we have discussed the convergence of the algorithm.Finally,the numerical experiments have been done to evaluate the performance of our model and algorithm when compared to the traditional TV model.