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.

翻译：彩色图像补全是计算机视觉领域的一个具有挑战性的问题，但近年来的研究表明，四元数表示在彩色图像处理中表现出色。这种表示方法将整幅彩色图像视为整体，能有效利用三个颜色通道间的耦合信息。因此，低秩四元数矩阵补全（LRQMC）算法受到了广泛关注。本文提出了一种基于四元数卡塔尔里亚尔分解（QQR）和四元数$L_{2,1}$-范数的方法，称为QLNM-QQR。该新方法通过避免计算大型四元数矩阵的QSVD，降低了计算复杂度。此外，我们还提出了QLNM-QQR方法的两种改进版本：一种是利用迭代重加权四元数$L_{2,1}$-范数最小化的增强型方法IRQLNM-QQR，另一种是融合稀疏正则化的QLNM-QQR-SR方法。在自然彩色图像和彩色医学图像上的实验表明，IRQLNM-QQR方法的性能优于QLNM-QQR，且所提出的QLNM-QQR-SR方法优于几种当前最先进的方法。