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Volume 13
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10.3390/math13101679
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications

by
Jia-Wei Huo
1,
Yun-Ze Xu
2 and
Zhuo-Heng He
2,3,*
1
Qianweichang College, Shanghai University, Shanghai 200444, China
2
Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
3
Sino-European School of Technology, Shanghai University, Shanghai 200444, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(10), 1679; https://doi.org/10.3390/math13101679
Submission received: 3 April 2025 / Revised: 15 May 2025 / Accepted: 18 May 2025 / Published: 20 May 2025
(This article belongs to the Special Issue Advanced Numerical Linear Algebra)
Versions Notes

Abstract

Quaternion tensor decompositions have recently been the center of focus due to their wide potential applications in color data processing. In this paper, we establish a simultaneous decomposition for a quaternion tensor quaternity under Einstein product. The decomposition brings the quaternity of four quaternion tensors into a canonical form, which only has 0 and 1 entries. The structure of the canonical form is discussed in detail. Moreover, the proposed decomposition is applied to a new framework of color video encryption and decryption based on discrete wavelet transform. This new approach can realize simultaneous encryption and compression with high security.
Keywords: tensor decomposition; quaternion algebra; quaternion tensor tensor decomposition; quaternion algebra; quaternion tensor

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MDPI and ACS Style

Huo, J.-W.; Xu, Y.-Z.; He, Z.-H. A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications. Mathematics 2025, 13, 1679. https://doi.org/10.3390/math13101679

AMA Style

Huo J-W, Xu Y-Z, He Z-H. A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications. Mathematics. 2025; 13(10):1679. https://doi.org/10.3390/math13101679

Chicago/Turabian Style

Huo, Jia-Wei, Yun-Ze Xu, and Zhuo-Heng He. 2025. "A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications" Mathematics 13, no. 10: 1679. https://doi.org/10.3390/math13101679

APA Style

Huo, J.-W., Xu, Y.-Z., & He, Z.-H. (2025). A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications. Mathematics, 13(10), 1679. https://doi.org/10.3390/math13101679

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