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Volume 14, Issue 3
Generalized Singular Value Decompositions for Tensors and Their Applications

Zhuo-Heng He, Michael K. Ng & Chao Zeng

DOI: 10.4208/nmtma.OA-2020-0132

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 692-713.

Published online: 2021-06

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  • Abstract

In this paper, we consider the generalized singular value decompositions for two tensors via the T-product. We investigate and discuss in detail the structures of the quotient singular value decomposition (T-QSVD) and product singular value decomposition (T-PSVD) for two tensors. The algorithms are presented with numerical examples illustrating the results. For applications, we consider color image watermarking processing with T-QSVD and T-PSVD. There are two advantages to T-QSVD and T-PSVD approaches on color watermark processing: two color watermarks can be processed simultaneously and only one key needs to be saved.

  • Keywords

Multilinear algebra, singular value decomposition, tensor SVD.

  • AMS Subject Headings

15A23, 15A69, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-692, author = {He , Zhuo-HengNg , Michael K. and Zeng , Chao}, title = {Generalized Singular Value Decompositions for Tensors and Their Applications}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {3}, pages = {692--713}, abstract = {

In this paper, we consider the generalized singular value decompositions for two tensors via the T-product. We investigate and discuss in detail the structures of the quotient singular value decomposition (T-QSVD) and product singular value decomposition (T-PSVD) for two tensors. The algorithms are presented with numerical examples illustrating the results. For applications, we consider color image watermarking processing with T-QSVD and T-PSVD. There are two advantages to T-QSVD and T-PSVD approaches on color watermark processing: two color watermarks can be processed simultaneously and only one key needs to be saved.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0132}, url = {http://global-sci.org/intro/article_detail/nmtma/19194.html} }
TY - JOUR T1 - Generalized Singular Value Decompositions for Tensors and Their Applications AU - He , Zhuo-Heng AU - Ng , Michael K. AU - Zeng , Chao JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 692 EP - 713 PY - 2021 DA - 2021/06 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0132 UR - https://global-sci.org/intro/article_detail/nmtma/19194.html KW - Multilinear algebra, singular value decomposition, tensor SVD. AB -

In this paper, we consider the generalized singular value decompositions for two tensors via the T-product. We investigate and discuss in detail the structures of the quotient singular value decomposition (T-QSVD) and product singular value decomposition (T-PSVD) for two tensors. The algorithms are presented with numerical examples illustrating the results. For applications, we consider color image watermarking processing with T-QSVD and T-PSVD. There are two advantages to T-QSVD and T-PSVD approaches on color watermark processing: two color watermarks can be processed simultaneously and only one key needs to be saved.

He , Zhuo-HengNg , Michael K. and Zeng , Chao. (2021). Generalized Singular Value Decompositions for Tensors and Their Applications. Numerical Mathematics: Theory, Methods and Applications. 14 (3). 692-713. doi:10.4208/nmtma.OA-2020-0132
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