Multi-Directional Tensor Average Rank Regularization for High-Order Tensor Completion

Recently, the high-order tensor Singular Value Decomposition (t-SVD) and the t-SVD rank has achieved great success in tensor completion. However, the t-SVD rank lacks the flexibility to capture the correlations between different modes of a high-order tensor. In addition, the Tensor Nuclear Norm (TNN), which is a convex surrogate of the t-SVD rank, applies the soft-thresholding operator to the singular value tensor in the transform domain, which will result in a bias. To overcome the mentioned shortcomings in the Low Rank Tensor Completion (LRTC) problem, we first propose a new high-order tensor average rank and its surrogate tensor φ norm. Then, we define the multi-directional tensor average rank and its surrogate multi-directional Tensor φ Norm (MDTN) by the tensor moveaxis operator to characterize the correlations between different modes of a tensor. ADMM based algorithm is designed and experiments on different visual data are carried out, experimental results show that our method outperforms the competing methods.