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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| Published in: | Applied mathematics and computation Vol. 512; p. 129780 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01.03.2026
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| ISSN: | 0096-3003 |
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| Abstract | •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. |
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| AbstractList | •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. |
| ArticleNumber | 129780 |
| Author | Wu, Fengsheng Li, Chaoqian Liu, Yonghe Miao, Jifei |
| Author_xml | – sequence: 1 givenname: Yonghe surname: Liu fullname: Liu, Yonghe email: 13625698503@163.com – sequence: 2 givenname: Fengsheng surname: Wu fullname: Wu, Fengsheng email: wufs1117@163.com – sequence: 3 givenname: Jifei surname: Miao fullname: Miao, Jifei email: jifmiao@163.com – sequence: 4 givenname: Chaoqian orcidid: 0000-0003-3754-8734 surname: Li fullname: Li, Chaoqian email: lichaoqian@ynu.edu.cn |
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| Cites_doi | 10.1007/s11075-018-0621-0 10.1016/j.cam.2018.04.019 10.1016/j.neucom.2024.127490 10.1016/j.patcog.2025.111580 10.1631/FITEE.1500334 10.1007/s11075-022-01310-1 10.1109/TIP.2015.2397314 10.1109/TRA.2003.820932 10.1016/j.aml.2023.108587 10.1137/19M1307329 10.1109/TSP.2018.2853137 10.1137/21M1418319 10.1007/s11075-023-01571-4 10.1016/j.inffus.2022.11.026 10.1007/s10092-017-0241-4 10.1007/s11075-023-01662-2 10.1016/j.aml.2021.107597 10.1016/j.aml.2023.108940 10.1007/s10915-024-02624-z 10.1016/j.sigpro.2022.108910 10.1137/090771806 10.1109/TIP.2022.3176133 10.1016/j.sigpro.2004.04.001 10.1007/s10915-022-01917-5 10.1007/s12190-023-01909-0 10.1007/BF01395873 10.1016/0024-3795(95)00543-9 10.1109/TIP.2019.2941319 10.1109/TII.2015.2397878 |
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| Keywords | Quaternion tensor singular value decomposition Randomized block Krylov iteration Qt-product Subspace-orbit random projection |
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| Snippet | •We investigate the third-order quaternion tensor singular value decomposition.•We propose a subspace-orbit randomized algorithm based on block Krylov... |
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| SubjectTerms | Qt-product Quaternion tensor singular value decomposition Randomized block Krylov iteration Subspace-orbit random projection |
| Title | A subspace-orbit randomized algorithm for quaternion tensor singular value decomposition based on Qt-product |
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