$L_{2,1}$-Norm Regularized Quaternion Matrix Completion Using Sparse
  Representation and Quaternion QR Decomposition
Juan Han Kit Ian Kou Jifei Miao Lizhi Liu Haojiang Li
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.