{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36550",
  "author_total": 3,
  "authors": [
    {
      "name": "Daochang Zhang"
    },
    {
      "name": "Yue Zhao"
    },
    {
      "name": "Jingqian Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8w1gk42zkge6p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36550",
  "fulltext_url": null,
  "id": "8w1gk42zkge6p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36550",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7224083659",
  "pdf_url": "https://arxiv.org/pdf/2610.36550",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8w1gk42zkge6p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36550",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36550"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Fast Algorithm for Quaternion Tensor Singular Value Decomposition under the QT-Product with Applications to Color Video Processing",
  "title_text": "A Fast Algorithm for Quaternion Tensor Singular Value Decomposition under the QT-Product with Applications to Color Video Processing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/8w1gk42zkge6p",
  "venue": "arXiv",
  "versions": []
}