A subspace-orbit randomized algorithm for quaternion tensor singular value decomposition based on Qt-product

•We investigate the third-order quaternion tensor singular value decomposition.•We propose a subspace-orbit randomized algorithm based on block Krylov iteration.•This algorithm can achieve the trade-off between computation time and accuracy.•We provide the deterministic and expected approximation er...

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 512; p. 129780
Main Authors:	Liu, Yonghe, Wu, Fengsheng, Miao, Jifei, Li, Chaoqian
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.03.2026
Subjects:	Qt-product Quaternion tensor singular value decomposition Randomized block Krylov iteration Subspace-orbit random projection Quaternion tensor singular value decomposition Randomized block Krylov iteration Qt-product Subspace-orbit random projection
ISSN:	0096-3003
Online Access:	Get full text
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Summary:	•We investigate the third-order quaternion tensor singular value decomposition.•We propose a subspace-orbit randomized algorithm based on block Krylov iteration.•This algorithm can achieve the trade-off between computation time and accuracy.•We provide the deterministic and expected approximation error bounds.•This algorithm is applied to color video compression and denoising.. Based on a subspace-orbit random projection method and a randomized block Krylov iteration approach, we propose a subspace-orbit randomized algorithm with the block Krylov iteration for third-order quaternion tensor singular value decomposition based on Qt-product. The deterministic and expected approximation error bounds for the proposed randomized algorithm are given. Numerical experiments using synthetic data and color video data are presented to demonstrate its feasibility and effectiveness.
ISSN:	0096-3003
DOI:	10.1016/j.amc.2025.129780