Low-Rank Tensor Completion by Approximating the Tensor Average Rank

Zhanliang Wang, Junyu Dong, Xinguo Liu, Xueying Zeng; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021, pp. 4612-4620

This paper focuses on the problem of low-rank tensor completion, the goal of which is to recover an underlying low-rank tensor from incomplete observations. Our method is motivated by the recently proposed t-product based on any invertible linear transforms. First, we define the new tensor average rank under the invertible real linear transforms. We then propose a new tensor completion model using a nonconvex surrogate to approximate the tensor average rank. This surrogate overcomes the discontinuity of the tensor average rank and alleviates the bias problem caused by the convex relaxation. Further, we develop an efficient algorithm to solve the proposed model and establish its convergence. Finally, experimental results on both synthetic and real data demonstrate the superiority of our method.