Color image completion is a challenging problem in computer vision. Despite the effectiveness of low-rank quaternion matrix completion (LRQMC) methods, their reliance on quaternion singular value decomposition (QSVD) makes them computationally expensive. We propose a novel method based on quaternion Qatar Riyal decomposition (QQR) and quaternion L-norm, named QLNM-QQR, which reduces computational complexity by avoiding the need for calculating the QSVD of large quaternion matrices. Furthermore, we introduce two improvements: IRQLNM-QQR, which utilizes iteratively reweighted quaternion L-norm minimization, and QLNM-QQR-SR, which integrates sparse regularization. Additionally, an analysis of the convergence of the proposed algorithms is conducted. Our experiments show that IRQLNM-QQR outperforms QLNM-QQR on both natural and medical color images. The QLNM-QQR-SR method achieves higher PSNR and SSIM values than state-of-the-art methods, with PSNR averaging 4–8 dB higher than non-sparse methods and 0.4 dB higher than the sparse-based TNN-SR method.