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arXiv · 2106.16073

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

Yating Zhang·Xiaoxia Guo·Pengpeng Xie·Zhengbang Cao
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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.

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Yating Zhang, Xiaoxia Guo, Pengpeng Xie, Zhengbang Cao. 2021-06-30. CS decomposition and GSVD for tensors based on the T-product. https://arxiv.org/abs/2106.16073

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