  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.
