Low tubal rank tensor completion based on singular value factors

Inspired by the definition of tensor-tensor product and tensor tubal rank, a randomized singular value decomposition of tensor is presented in this paper. Based on tensor singular value decomposition (t-SVD) and tensor randomized singular value decomposition (t-RSVD), we obtain two efficient algorithms to solve tensor completion problem. We also propose the adaptive rank method to adjust the tubal rank of tensor. The main advantage of the random projection-based t-RSVD is to cut down the computing time in consideration of large-scale problems. In the optimization process, the alternating minimization algorithm is employed to solve the tensor completion problem. Finally, numerical experiment results indicate that the t-RSVD is competitive and consumes less time than the t-SVD. The efficiency and feasibility of our methods are illustrated by the image and video recovery.