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Matrix completion is one of the most challenging problems in computer vision.Recently, quaternion representations of color images have achieved competitiveperformance in many fields. Because it treats the color image as a whole, thecoupling information between the three channels of the color image is betterutilized. Due to this, low-rank quaternion matrix completion (LRQMC) algorithmshave gained considerable attention from researchers. In contrast to thetraditional quaternion matrix completion algorithms based on quaternionsingular value decomposition (QSVD), we propose a novel method based onquaternion Qatar Riyal decomposition (QQR). In the first part of the paper, anovel method for calculating an approximate QSVD based on iterative QQR isproposed (CQSVD-QQR), whose computational complexity is lower than that ofQSVD. The largest $r \ (r>0)$ singular values of a given quaternion matrix canbe computed by using CQSVD-QQR. Then, we propose a new quaternion matrixcompletion method based on CQSVD-QQR which combines low-rank and sparse priorsof color images. Experimental results on color images and color medical imagesdemonstrate that our model outperforms those state-of-the-art methods.

Low Rank Quaternion Matrix Completion Based on Quaternion QR Decomposition and Sparse Regularizer