A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications
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 fo...
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MDPI AG
2025-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/10/1679 |
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| author | Jia-Wei Huo Yun-Ze Xu Zhuo-Heng He |
| author_facet | Jia-Wei Huo Yun-Ze Xu Zhuo-Heng He |
| author_sort | Jia-Wei Huo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6a769308d4f6475fa3f88c146b8dab2a |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6a769308d4f6475fa3f88c146b8dab2a2025-08-20T01:56:19ZengMDPI AGMathematics2227-73902025-05-011310167910.3390/math13101679A Simultaneous Decomposition for a Quaternion Tensor Quaternity with ApplicationsJia-Wei Huo0Yun-Ze Xu1Zhuo-Heng He2Qianweichang College, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, ChinaQuaternion 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.https://www.mdpi.com/2227-7390/13/10/1679tensor decompositionquaternion algebraquaternion tensor |
| spellingShingle | Jia-Wei Huo Yun-Ze Xu Zhuo-Heng He A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications Mathematics tensor decomposition quaternion algebra quaternion tensor |
| title | A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications |
| title_full | A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications |
| title_fullStr | A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications |
| title_full_unstemmed | A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications |
| title_short | A Simultaneous Decomposition for a Quaternion Tensor Quaternity with Applications |
| title_sort | simultaneous decomposition for a quaternion tensor quaternity with applications |
| topic | tensor decomposition quaternion algebra quaternion tensor |
| url | https://www.mdpi.com/2227-7390/13/10/1679 |
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