A new version of simple low rank tensor completion via TV regularization

Tensor completion problem by minimization of the rank of tensor, leads to an appropriate solution, however, it gives a non-convex objective function that generates an NP-hard problem. To solve this problem, the trace norm is applied, which is a convex function. Despite the good performance, the recovered images using trace norm methods are mostly reconstructed along with horizontal or vertical lines. To overcome this problem, the total variation can be used. In this paper, to increase the accuracy of the simple low-rank tensor completion algorithm, a total variation regularization is added to it, which causes the loss of horizontal or vertical lines in the recovered images and also increases the recovery accuracy.