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

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

Abstract: 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.