A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications

Jia-Wei Huo, Yun-Ze Xu and Zhuo-Heng He ()
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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

Mathematics, 2025, vol. 13, issue 10, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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