论文标题
基于四元素QR分解和稀疏正规器的低等级四元基质矩阵完成
Low Rank Quaternion Matrix Completion Based on Quaternion QR Decomposition and Sparse Regularizer
论文作者
论文摘要
矩阵完成是计算机视觉中最具挑战性的问题之一。最近，彩色图像的四元代表在许多领域都取得了竞争性能。因为它整体上都将颜色图像视为，所以更好地利用了颜色图像的三个通道之间的耦合信息。因此，低级四元基质完成（LRQMC）算法引起了研究人员的极大关注。与基于四个元素奇异值分解（QSVD）的传统四元基质完成算法相反，我们提出了一种基于Qatar riyal分解（QQR）的新方法。在本文的第一部分中，提出了一种基于迭代QQR计算近似QSVD的新方法（CQSVD-QQR），其计算复杂性低于QSVD。可以通过使用CQSVD-QQR计算给定Quaternion矩阵的最大$ r \（r> 0）$奇异值。然后，我们基于CQSVD-QQR提出了一种新的Quaternion矩阵完成方法，该方法结合了颜色图像的低级和稀疏先验。颜色图像和彩色医学图像的实验结果表明，我们的模型表现优于这些最新方法。
Matrix completion is one of the most challenging problems in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. Because it treats the color image as a whole, the coupling information between the three channels of the color image is better utilized. Due to this, low-rank quaternion matrix completion (LRQMC) algorithms have gained considerable attention from researchers. In contrast to the traditional quaternion matrix completion algorithms based on quaternion singular value decomposition (QSVD), we propose a novel method based on quaternion Qatar Riyal decomposition (QQR). In the first part of the paper, a novel method for calculating an approximate QSVD based on iterative QQR is proposed (CQSVD-QQR), whose computational complexity is lower than that of QSVD. The largest $r \ (r>0)$ singular values of a given quaternion matrix can be computed by using CQSVD-QQR. Then, we propose a new quaternion matrix completion method based on CQSVD-QQR which combines low-rank and sparse priors of color images. Experimental results on color images and color medical images demonstrate that our model outperforms those state-of-the-art methods.
