  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.
