A Fast Algorithm for Quaternion Tensor Singular Value Decomposition under the QT-Product with Applications to Color Video Processing
Abstract
Based on the complex representation of quaternion matrices, this paper revisits the quaternion tensor singular value decomposition (QT-SVD) under the QT-product and establishes the corresponding z-block circulant matrix decomposition. We develop an efficient implementation of the QT-SVD. Numerical experiments show that this implementation is substantially faster than QT-SVD based on the quaternion matrix SVD approach \cite[Theorem~2.3]{AMLzhang2022} while maintaining high numerical accuracy. We further apply the QT-SVD to color video encryption and reconstruction. Experiments on five DAVIS video sequences show that the QT-SVD achieves higher reconstruction quality and shorter decomposition times than the quaternion T-SVD \cite{tsvdarxiv} under the same processing procedure. Both methods exhibit comparable ciphertext statistics and differential sensitivity, while the QT-SVD introduces less additional distortion under the tested input perturbations.
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BibTeX
@misc{zhang2026fast,
title = {{A Fast Algorithm for Quaternion Tensor Singular Value Decomposition under the QT-Product with Applications to Color Video Processing}},
author = {Daochang Zhang and Yue Zhao and Jingqian Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36550},
eprint = {2610.36550},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36550},
}
RIS
TY - UNPB
TI - A Fast Algorithm for Quaternion Tensor Singular Value Decomposition under the QT-Product with Applications to Color Video Processing
AU - Daochang Zhang
AU - Yue Zhao
AU - Jingqian Li
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36550
UR - https://arxiv.org/abs/2610.36550
AB - Based on the complex representation of quaternion matrices, this paper revisits the quaternion tensor singular value decomposition (QT-SVD) under the QT-product and establishes the corresponding z-block circulant matrix decomposition. We develop an efficient implementation of the QT-SVD. Numerical experiments show that this implementation is substantially faster than QT-SVD based on the quaternion matrix SVD approach \cite[Theorem~2.3]{AMLzhang2022} while maintaining high numerical accuracy. We further apply the QT-SVD to color video encryption and reconstruction. Experiments on five DAVIS video sequences show that the QT-SVD achieves higher reconstruction quality and shorter decomposition times than the quaternion T-SVD \cite{tsvdarxiv} under the same processing procedure. Both methods exhibit comparable ciphertext statistics and differential sensitivity, while the QT-SVD introduces less additional distortion under the tested input perturbations.
ER -