An algorithm for nonconvex functional minimization and applications to image restoration

Bartomeu Coll, Joan Duran, Catalina Sbert

Abstract: In this paper, we propose a new dual algorithm for the minimization of discrete nonconvex functionals, called half-linear regularization. Our approach alternates the calculation of a explicit weight with the minimization of a convex functional with respect to the solution. This minimization corresponds to the weighted total variation which is solved via the well-known Chambolle's algorithm. Finally, we present experimental results by applying it to some image restoration problems as denoising and deconvolution.