CS decomposition and GSVD for tensors based on the T-product
Numerical Analysis
2021-07-01 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2106.16073,
title = {CS decomposition and GSVD for tensors based on the T-product},
author = {Yating Zhang and Xiaoxia Guo and Pengpeng Xie and Zhengbang Cao},
journal= {arXiv preprint arXiv:2106.16073},
year = {2021}
}