| 丁小建,黄宝华.基于四元数离散余弦变换的张量奇异值分解[J].井冈山大学自然版,2025,46(3):8-14 |
| 基于四元数离散余弦变换的张量奇异值分解 |
| TENSOR SINGULAR VALUE DECOMPOSITION BASED ON QUATERNION DISCRETE COSINE TRANSFORM |
| 投稿时间：2024-11-12 修订日期：2024-12-26 |
| DOI：10.3969/j.issn.1674-8085.2025.03.002 |
| 中文关键词: 四元数离散余弦变换 Toeplitz-plus-Hankel矩阵 块对角化 张量奇异值分解 |
| 英文关键词: quaternion discrete cosine transform Toeplitz-plus-Hankel matrix block diagonalization tensor singular value decomposition |
| 基金项目:国家自然科学基金青年项目(12001211) |
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| 摘要点击次数: 34 |
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| 中文摘要: |
| 本研究定义了一类四元数离散余弦变换矩阵，实现了四元数Toeplitz-plus-Hankel矩阵对角化，建立了基于四元数离散余弦变换的张量奇异值分解。数值实验表明，该算法的可行性和高效性。此外，还给出了与彩色视频压缩相关的应用，以检验所提算法在实际问题中的有效性。 |
| 英文摘要: |
| In this paper, a quaternion discrete cosine transform matrix is defined, the quaternion Toeplitz-plus-Hankel matrix is diagonalized, and the quaternion tensor singular value decomposition based on quaternion discrete cosine transform is established. Numerical experiments demonstrate the feasibility and efficiency of the proposed algorithm. Additionally, applications related to color video compression are provided to demonstrate the effectiveness of the proposed algorithm in practical problems. |
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