Tensor Completion From Structurally-Missing Entries by Low-TT-Rankness and Fiber-Wise Sparsity

Most tensor completion methods assume that missing entries are randomly distributed in incomplete tensors, and the low-rank prior or its variants are used to well pose the problem. However, this could be violated in practical applications where missing entries are not only randomly but also structurally distributed. To remedy this, this paper proposes a novel tensor completion method equipped with double priors on the latent tensor, named tensor completion from structurally-missing entries by low tensor train (TT) rankness and fiber-wise sparsity. In the proposed model, the underlying tensor is regularized by a low-TT-rankness prior to exploit the inter-fibers/-slices correlations, and its fibers are regularized by a sparsity prior under dictionaries to exploit intra-fibers correlations. The proposed model is solved by an alternating direction method under the augmented Lagrangian multiplier framework. Experimental results on both synthetic and real data demonstrate the effectiveness and superiority of the proposed model in completing tensors with both random and structural missing entries, compared with state-of-the-art tensor completion approaches.