Leveraging Tensor Subspace Prior: Enhanced Sum of Nuclear Norm Minimization for Tensor Completion

Tensor completion has attracted increasing attention in signal processing, computer vision, and biomedical engineering. By using nuclear norm minimization, a tensor completion problem can be converted into a convex program and enjoys properties gained from matrix completion. The low rank property has been widely used for tensor/matrix completion. However, the prior subspace information can also be utilized, which has been ignored and does not exhibit its full power in the existing formulation. In this paper, we propose a new framework leveraging tensor subspace prior for the sum of nuclear norm (SNN) minimization, which supports a range of tensor decompositions. By using the knowledge of the self-prior (SP)/nonself-prior (NSP) and further designing an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM), the performance of tensor completion can be enhanced. The superiority of the proposed method is verified by extensive numerical experiments.