Randomized quaternion tensor UTV decompositions for color image and color video processing

作     者：Yang, Liqiao Miao, Jifei Jiang, Tai-Xiang Zhang, Yanlin Kou, Kit Ian 

作者机构：Southwestern Univ Finance & Econ Res Inst Digital Econ & Interdisciplinary Sci Sch Comp & Artificial Intelligence Chengdu 611130 Peoples R China Univ Macau Fac Sci & Technol Dept Math Macau 999078 Peoples R China 

出 版 物：《PATTERN RECOGNITION》 (Pattern Recogn.)

年 卷 期：2025年第165卷

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：University of Macau [MYRG-GRG202400290-FST-UMDF, MYRG-CRG2024-00046-FHS] Sichuan Science and Technology Program [2024ZYD0147] Natural Science Foundation of Xinjiang Uygur Autonomous Region [2024D01A18] Graduate Representative Achievement Cultivation Project of Southwest University of Finance and Economics [JGS2024069] Guanghua Talent Project of Southwest University of Finance and Economics [JGS2024069] 

主　　题：Quaternion UTV Randomized algorithm Quaternion tensor Color image processing Low-rank approximation 

摘      要：In this paper, we propose novel quaternion matrix UTV (QUTV) and quaternion tensor UTV (QTUTV) decomposition methods, specifically designed for color image and video processing. We begin by defining both QUTV and QTUTV decompositions and provide detailed algorithmic descriptions. To enhance computational efficiency, we introduce randomized versions of these decompositions using random sampling from the quaternion normal distribution, which results in cost-effective and interpretable solutions. Extensive numerical experiments demonstrate that the proposed algorithms significantly improve computational efficiency while maintaining relative errors comparable to existing decomposition methods. These results underscore the strong potential of quaternion-based decompositions for real-world color image and video processing applications. Theoretical findings further support the robustness of the proposed methods, providing a solid foundation for their widespread use in practice.