An Efficient Non-convex Mixture Method for Low-rank Tensor Completion

For the problem of low-rank tensor completion, rank estimation plays an extremely important role. And among some outstanding researches, nuclear norm is often used as a substitute of rank in the optimization due to its convex property. However, recent advances show that some non-convex functions could approximate the rank better, which can significantly improve the precision of the algorithm. While, the complexity of non-convex functions also lead to much higher computation cost, especially in handling large scale matrices from the mode-n unfolding of a tensor. This paper proposes a mixture model for tensor completion by combining logDet function with Tucker decomposition to achieve a better performance in precision and a lower cost in computation as well. In the implementation of the method, alternating direction method of multipliers (ADMM) is employed to obtain the optimal tensor completion. Experiments on image restoration are carried out to validate the effective and efficiency of the method.