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.

翻译：本文介绍了三阶简化双四元数张量在彩色视频处理中的应用。我们首先通过一种新的Ht-乘积，开发了计算三阶简化双四元数张量奇异值分解（SVD）的算法。作为理论应用，我们定义了三阶简化双四元数张量的Moore-Penrose逆，并给出了其表征。此外，我们讨论了简化双四元数张量方程 $\mathcal{A}\ast_{Ht} \mathcal{X}=\mathcal{B}$ 的一般解（或Hermitian解）及其最小二乘解。最后，我们利用该SVD对彩色视频进行压缩，实验数据表明，我们的方法比对比方案更快。