A Non-convex Regularization Fusing Low-rankness and Smoothness for Tensor Recovery

Recently, the tensor recovery problem has witnessed significant advancements with the non-convex relaxation methods, compared with convex relaxation methods. In this article, we propose a novel non-convex relaxation method for the low-rank tensor completion and tensor robust principal component analysis, which uses the global low-rankness and local smoothness of the recovered tensor. And we further build the solving algorithms of the proposed models based on the well-known ADMM and the linear approximation method. The better performance of our proposed method is unequivocally validated by extensive numerical experiments, compared to other state-of-the-art methods in terms of both numerical accuracy and visual quality. We further propose ADMM algorithms with fine convergence to solve the proposed models.