The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix approximation is sometimes considerable due to the computation of the quaternion singular value decomposition (QSVD), which limits their application to real large-scale data. To address this deficiency, an efficient quaternion matrix CUR (QMCUR) method for low-rank approximation is suggested, which provides significant acceleration in color image processing. We first explore the QMCUR approximation method, which uses actual columns and rows of the given quaternion matrix, instead of the costly QSVD. Additionally, two different sampling strategies are used to sample the above-selected columns and rows. Then, the perturbation analysis is performed on the QMCUR approximation of noisy versions of low-rank quaternion matrices. Extensive experiments on both synthetic and real data further reveal the superiority of the proposed algorithm compared with other algorithms for getting low-rank approximation, in terms of both efficiency and accuracy.
Pass-efficient Randomized Algorithms for Low-rank Approximation of Quaternion Matrices
Innopolis University（伊诺波利斯大学）；Research Center of the Artificial Intelligence Institute, and Lab of Machine Learning and Knowledge Representation, Innopolis University（伊诺波利斯大学人工智能研究所研究中心及机器学习与知识表示实验室）
Quaternion Maximum-Volume Submatrix Selection with Applications to Multichannel Imaging and Visual Data
Institute of Data Science and Artificial Intelligence, Innopolis University（因诺波利斯大学数据科学与人工智能研究所）；Department of Mathematics, Faculty of Science, Hong Kong Baptist University, Hong Kong, China（香港浸会大学理学院数学系）
Non-Local Robust Quaternion Matrix Completion for Color Images and Videos Inpainting
Jiangsu Normal University（江苏师范大学）；Inner Mongolia University（内蒙古大学）；The University of Hong Kong（香港大学）；University of Electronic Science and Technology of China（电子科技大学）
