l0NHTV : A Non-convex Hybrid Total Variation Regularization Method for Image Restoration

Image restoration is a serious inverse problem, and the regularization method is recognized as an effective method. In this paper, a l(0) non-convex hybrid total variation(NHTV) regularization method is proposed, and the TV-based restoration problem is solved by using l(0) norm data fidelity. In order to effectively tackle the proposed nonconvex and non-smooth optimization problem, we first express this problem as a Mathematical Program with Equilibrium Constraints(MPEC), and then a proximal Alternating Direction Method of Multipliers(PADMM) is adopted to solve this problem. Numerical simulations verify the effectiveness of our proposed method. The comparations with other convex TV-based regularization methods are also conducted, which clearly show that this method can achieve better suppression of the staircase effect, effectively preserve the edge information and therefore obtain a higher signal-to-noise ratio.