A nonconvex model with minimax concave penalty for image restoration (Q2420696)

A nonconvex model is proposed for image restoration with a minimax concave penalty (MCP) that enjoys good performance for sparse signal recovery. The existence of the global minimizer of the model is proven using the approach that can be applied to a class of nonconvex penalized models which do not necessarily have coercive penalties. Then the model is solved by using the alternating direction method of multipliers algorithm similar to that by \textit{R. T. Rockafellar} [Math. Oper. Res. 1, 97--116 (1976; Zbl 0402.90076)]. Under a mild condition the global subsequential convergence of the algorithm is established with properly chosen parameters. Numerical experiments demonstrate that the MCP model outperforms the TV model in terms of efficiency and accuracy.