Abstract
A natural image u is often sparse under a given transformation W, one can use $$L_0$$ norm of Wu as a regularisation term in image reconstructions. Since minimizing the $$L_0$$ norm is a NP hard problem, the $$L_1$$ norm is widely used as an replacement. However, recent studies show that nonconvex penalties, e.g., MCP, enjoy better performance for sparse signal recovery. In this paper, we propose a nonconvex model for image restoration with a minimax concave penalty (MCP). First we establish the existence of a global minimizer for the nonconvex model. Then we solve this model by using the alternating direction method of multipliers algorithm. The convergence of the proposed algorithm is analysed with properly chosen parameters. Numerical experiments show that the MCP model outperforms TV model in terms of efficiency and accuracy.
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