Simultaneous Visual Data Completion and Denoising Based on Tensor Rank and Total Variation Minimization and Its Primal-Dual Splitting Algorithm

Tensor completion has attracted attention because of its promising ability and generality. However, there are few studies on noisy scenarios which directly solve an optimization problem consisting of a "noise inequality constraint". In this paper, we propose a new tensor completion and denoising model including tensor total variation and tensor nuclear norm minimization with a range of values and noise inequalities. Furthermore, we developed its solution algorithm based on a primal-dual splitting method, which is computationally efficient as compared to tensor decomposition based non-convex optimization. Lastly, extensive experiments demonstrated the advantages of the proposed method for visual data retrieval such as for color images, movies, and 3D-volumetric data.