Singular value decompositions of third-order reduced biquaternion tensors
<|reference_start|>Singular value decompositions of third-order reduced biquaternion tensors: 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.<|reference_end|>
@article{yu2024singular,
    title={Singular value decompositions of third-order reduced biquaternion
  tensors},
    author={Cui-E Yu, Xin Liu, Yang Zhang},
    journal={arXiv preprint arXiv:2403.01690},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.01690},
    primaryClass={math.NA cs.NA}
}