Matrix completion is a challenging problem in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. The information on the coupling between the three channels of the color image is better utilized since the color image is treated as a whole. Due to this, researcher interest in low-rank quaternion matrix completion (LRQMC) algorithms has grown significantly. In contrast to the traditional quaternion matrix completion algorithms that rely on quaternion singular value decomposition (QSVD), we propose a novel method based on quaternion Qatar Riyal decomposition (QQR). First, a novel approach (CQSVD-QQR) to computing an approximation of QSVD based on iterative QQR is put forward, which has lower computational complexity than QSVD. CQSVD-QQR can be employed to calculate the greatest r(r>0) singular values of a given quaternion matrix. Following that, we propose a novel quaternion matrix completion approach based on CQSVD-QQR which combines low-rank and sparse priors of color images. Furthermore, the convergence of the algorithm is analyzed. Our model outperforms those state-of-the-art approaches following experimental results on natural color images and color medical images.

中文翻译：

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基于近似四元数 SVD 和稀疏正则化器的低秩四元数矩阵补全


矩阵完成是计算机视觉中一个具有挑战性的问题。最近，彩色图像的四元数表示在许多领域都取得了有竞争力的性能。由于彩色图像被视为一个整体，因此可以更好地利用彩色图像的三个通道之间的耦合信息。因此，研究人员对低秩四元数矩阵完成 （LRQMC） 算法的兴趣显著增加。与依赖于四元数奇异值分解 （QSVD） 的传统四元数矩阵完成算法相比，我们提出了一种基于四元数卡塔尔里亚尔分解 （QQR） 的新方法。首先，提出了一种基于迭代 QQR 计算 QSVD 近似的新方法 （CQSVD-QQR），该方法的计算复杂度低于 QSVD。CQSVD-QQR 可用于计算给定四元数矩阵的最大 r（r>0） 奇异值。然后，我们提出了一种基于 CQSVD-QQR 的新型四元数矩阵完成方法，该方法结合了彩色图像的低秩和稀疏先验。此外，分析了算法的收敛性。在自然彩色图像和彩色医学图像的实验结果之后，我们的模型优于那些最先进的方法。