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.

翻译：本文引申出对正向强压的CS分解(T-SD)和通过T产品对两个发压器(T-GSVD)的通用单值分解(T-GSVD),对这两个分解的结构进行了详细分析,并与矩阵案例的结构相一致。然后分别提出了相应的算法。最后,T-GSVD可用于明确表达对 Exor Tikhonov 的正规化的解决方案。数字实例表明T-GSVD在解决图像恢复问题方面的有效性。