Singular value decompositions of third-order reduced biquaternion tensors
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916488879800320 |
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| author | Yu, Cui-E Liu, Xin Zhang, Yang |
| author_facet | Yu, Cui-E Liu, Xin Zhang, Yang |
| contents | In this paper, we introduce the applications of third-order reduced biquaternion tensors in color video processing. We first develop algorithms for computing the singular value decomposition (SVD) of a third-order reduced biquaternion tensor via a new Ht-product. As theoretical applications, we define the Moore-Penrose inverse of a third-order reduced biquaternion tensor and develop its characterizations. In addition, we discuss the general (or Hermitian) solutions to reduced biquaternion tensor equation $\mathcal{A}\ast_{Ht} \mathcal{X}=\mathcal{B}$ as well as its least-square solution. Finally, we compress the color video by this SVD, and the experimental data shows that our method is faster than the compared scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular value decompositions of third-order reduced biquaternion tensors Yu, Cui-E Liu, Xin Zhang, Yang Numerical Analysis In this paper, we introduce the applications of third-order reduced biquaternion tensors in color video processing. We first develop algorithms for computing the singular value decomposition (SVD) of a third-order reduced biquaternion tensor via a new Ht-product. As theoretical applications, we define the Moore-Penrose inverse of a third-order reduced biquaternion tensor and develop its characterizations. In addition, we discuss the general (or Hermitian) solutions to reduced biquaternion tensor equation $\mathcal{A}\ast_{Ht} \mathcal{X}=\mathcal{B}$ as well as its least-square solution. Finally, we compress the color video by this SVD, and the experimental data shows that our method is faster than the compared scheme. |
| title | Singular value decompositions of third-order reduced biquaternion tensors |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.01690 |