Adaptive non-convex non-smooth regularization for image restoration based on spatial information

Non-convex non-smooth (NCNS) regularization has advantages over convex regularization for restoring images, but it may lead to challenging computation. In this paper, an adaptive non-convex non-smooth (ANCNS) regularization is proposed for image restoration by using the spatial information indicator. Moreover, an efficient numerical algorithm for solving the resulting minimization problem is provided by applying the variable splitting and the penalty techniques. Finally, its advantages are shown in deblurring edges and restoring fines of image simultaneously in experiments.