Truncated nuclear norm minimization for tensor completion

In this paper, a tensor n-mode matrix unfolding truncated nuclear norm is proposed, which is extended from the matrix truncated nuclear norm, to tensor completion problem. The alternating direction method of multipliers is utilized to solve this optimization problem. Meanwhile, the original two-step solution of the matrix truncated nuclear norm is reduced to one step. Employing the intermediate results returned by singular value shrinkage operator, rank information of each tensor unfolding matrix is not required and thus the computational complexity of the devised approach is not demanding. Computer simulation results demonstrate the effectiveness of the proposed method.