Color image completion is a challenging problem in computer vision, but
recent research has shown that quaternion representations of color images
perform well in many areas. These representations consider the entire color
image and effectively utilize coupling information between the three color
channels. Consequently, low-rank quaternion matrix completion (LRQMC)
algorithms have gained significant attention. We propose a method based on
quaternion Qatar Riyal decomposition (QQR) and quaternion $L_{2,1}$-norm called
QLNM-QQR. This new approach reduces computational complexity by avoiding the
need to calculate the QSVD of large quaternion matrices. We also present two
improvements to the QLNM-QQR method: an enhanced version called IRQLNM-QQR that
uses iteratively reweighted quaternion $L_{2,1}$-norm minimization and a method
called QLNM-QQR-SR that integrates sparse regularization. Our experiments on
natural color images and color medical images show that IRQLNM-QQR outperforms
QLNM-QQR and that the proposed QLNM-QQR-SR method is superior to several
state-of-the-art methods.

颜色图像完成是计算机视觉中的一个具有挑战性的问题，近期的研究表明，四元数表示的彩色图像在很多领域表现出色。我们提出一种基于四元数卡塔尔里亚尔分解（QQR）和四元数 L2,1 范数的方法，称为 QLNM-QQR。我们在 QLNM-QQR 方法上还提出了两个改进，包括使用迭代重新加权的四元数 L2,1 范数最小化的增强版本 IRQLNM-QQR 和集成稀疏正则化的方法 QLNM-QQR-SR。我们对自然彩色图像和彩色医学图像进行的实验表明，IRQLNM-QQR 优于 QLNM-QQR，并且所提出的 QLNM-QQR-SR 方法优于几种最先进的方法。