Weighted tensor nuclear norm minimization for tensor completion using tensor-SVD

In this paper, we consider the tensor completion problem, which aims to estimate missing values from limited information. Our model is based on the recently proposed tensor-SVD, which uses the relationships among the color channels in an image or video recovery problem. To improve the availability of the model, we propose the weighted tensor nuclear norm whose weights are fixed in the algorithm, study its properties and prove the Karush-Kuhn-Tucker (KKT) conditions of the proposed algorithm. We conduct extensive experiments to verify the recovery capability of the proposed algorithm. The experimental results demonstrate improvements in computation time and recovery effect compared with related methods.