Lu Xiaoqiang, Gong Tieliang, Yan Pingkun, Yuan Yuan, Li Xuelong
Center for Optical Imagery Analysis and Learning, State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, China.
IEEE Trans Syst Man Cybern B Cybern. 2012 Jun;42(3):939-49. doi: 10.1109/TSMCB.2012.2185490. Epub 2012 Feb 15.
Recently, much attention has been drawn to the problem of matrix completion, which arises in a number of fields, including computer vision, pattern recognition, sensor network, and recommendation systems. This paper proposes a novel algorithm, named robust alternative minimization (RAM), which is based on the constraint of low rank to complete an unknown matrix. The proposed RAM algorithm can effectively reduce the relative reconstruction error of the recovered matrix. It is numerically easier to minimize the objective function and more stable for large-scale matrix completion compared with other existing methods. It is robust and efficient for low-rank matrix completion, and the convergence of the RAM algorithm is also established. Numerical results showed that both the recovery accuracy and running time of the RAM algorithm are competitive with other reported methods. Moreover, the applications of the RAM algorithm to low-rank image recovery demonstrated that it achieves satisfactory performance.
最近，矩阵补全问题受到了广泛关注，该问题出现在包括计算机视觉、模式识别、传感器网络和推荐系统等多个领域。本文提出了一种名为鲁棒交替最小化（RAM）的新算法，它基于低秩约束来补全未知矩阵。所提出的RAM算法能够有效降低恢复矩阵的相对重构误差。与其他现有方法相比，在数值上更容易最小化目标函数，并且对于大规模矩阵补全更稳定。它对于低秩矩阵补全具有鲁棒性和高效性，并且还建立了RAM算法的收敛性。数值结果表明，RAM算法的恢复精度和运行时间与其他已报道的方法相比具有竞争力。此外，RAM算法在低秩图像恢复中的应用表明它取得了令人满意的性能。
