Abstract :

Nonconvex nonsmooth regularization has advantages over convex regularization for restoring images with neat edges. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, we study a fast nonconvex nonsmooth minimization method for image restoration and reconstruction. Our theoretical results show that the solution of the nonconvex nonsmooth minimization problem can be composed of constant regions surrounded by closed contours and neat edges. The main aim of this paper is to develop a fast minimization algorithm to solve the nonconvex nonsmooth minimization problem. Our experimental results show that the effectiveness and efficiency of the proposed method.