Nonconvex and nonsmooth total generalized variation model for image restoration

Abstract In this paper, we propose a nonconvex and nonsmooth total generalized variation (TGV) model for image restoration, which can provide an even sparser representation of the variation of the image function than the traditional TGV model that uses convex l 1 norm to measure the variation. New model combines the advantages of nonconvex regularization and TGV regularization, and can preserve image edges well and simultaneously alleviate the staircase effects often arising in the total variation based models. Two different iteratively reweighed algorithms are introduced to numerically solve the proposed nonconvex and nonsmooth TGV model. Numerical results show that the proposed model is effective in edge-preserving and staircase-reduction in image restoration. In addition, compared with several state-of-the-art variational models, the proposed model has the best performance in terms of PSNR and MSSIM values.