Image cartoon-texture decomposition by a generalized non-convex low-rank minimization method

Image cartoon -texture decomposition is an important problem in image processing. In recent years, by exploiting low -rank priors of images, low -rank minimization methods have been widely adopted for image cartoon -texture decomposition. Since matrix rank minimization is an NP -hard problem, the convex nuclear norm is often used as a substitute for the matrix's rank to realize the low -rank minimization methods. In this paper, we utilize a generalized non -convex surrogate of the matrix rank function to develop a novel low -rank minimization model for image cartoon -texture decomposition. We design a proximal alternating algorithm to solve the non -convex model and further demonstrate the global convergence of the algorithm. Numerical experiments illustrate that the proposed method can show much better performances than the existing state-of-the-art methods for image cartoon -texture decomposition.