Adaptive Nonconvex Nonsmooth Regularization for Image Restoration Based on Spatial Information

Image restoration is an ill-posed problem that requires regularization to solve. Many existing regularization terms in the literature are the convex function. However, nonconvex nonsmooth regularization has advantages over convex regularization for restoring images, but its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, an adaptive nonconvex nonsmooth 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.