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Decomposition for a Quaternion Tensor Triplet with Applications

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Abstract

In this paper, we investigate and discuss in detail the structure and properties of product singular value decomposition for a quaternion tensor triplet under Einstein product (higher-order PSVD). As an application, we consider color video watermark processing with this higher-order PSVD.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant no. 11801354 and 11971294). The authors would also like to thank the anonymous referees for careful reading of the manuscript and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Zhuo-Heng He

  2. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA

    Carmeliza Navasca

  3. Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, USA

    Xiang-Xiang Wang

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  1. Zhuo-Heng He
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This article is part of the Topical Collection on Proceedings ICCA 12, Hefei, 2020, edited by Guangbin Ren, Uwe Kähler, Rafal Ablamowicz, Fabrizio Colombo, Pierre Dechant, Jacques Helmstetter, G. Stacey Staples, Wei Wang.

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He, ZH., Navasca, C. & Wang, XX. Decomposition for a Quaternion Tensor Triplet with Applications. Adv. Appl. Clifford Algebras 32, 9 (2022). https://doi.org/10.1007/s00006-021-01195-8

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