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A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications

Author

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  • Jia-Wei Huo

    (Qianweichang College, Shanghai University, Shanghai 200444, China)

  • Yun-Ze Xu

    (Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China)

  • Zhuo-Heng He

    (Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
    Sino-European School of Technology, Shanghai University, Shanghai 200444, China)

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.

Suggested Citation

  • Jia-Wei Huo & Yun-Ze Xu & Zhuo-Heng He, 2025. "A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications," Mathematics, MDPI, vol. 13(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1679-:d:1660162
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    References listed on IDEAS

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    1. Ivan I. Kyrchei, 2018. "Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations," Journal of Mathematics, Hindawi, vol. 2018, pages 1-12, November.
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