CS decomposition and GSVD for tensors based on the T-product

Abstract: This paper derives the CS decomposition for orthogonal tensors (T-CSD) and the generalized singular value decomposition for two tensors (T-GSVD) via the T-product. The structures of the two decompositions are analyzed in detail and are consistent with those for matrix cases. Then the corresponding algorithms are proposed respectively. Finally, T-GSVD can be used to give the explicit expression for the solution of tensor Tikhonov regularization. Numerical examples demonstrate the effectiveness of T-GSVD in solving image restoration problems.