Abstract: The problem of low-rank matrix completion has attracted massive attention in various engineering fields such as machine learning, image processing and video denoising. Assuming the data are low-rank, missing entries can be estimated in matrices by matrix completion algorithms, and the best approximation which fixes the constraints is produced. However, most matrix completion methods usually result in unsatisfactory reconstruction accuracy with adding non-Gaussian noise. This paper proposes a new robust algorithm for matrix completion considering some traditional methods which can enhance the robustness and avoid fitting. This paper can identify the location of outliers and replace them with approximate data, reducing the influence of outliers to the result, and enhancing the accuracy of the reconstruction. Simulated data and real data show that the algorithm is good at robustness and accuracy when the data sets are polluted by the non-Gaussian noise.

Key words: matrix completion, low-rank matrix recovery, outliers, robustness

摘要： 低秩矩阵补全的相关问题在机器学习、图像处理、视频去噪等领域受到极大关注，在假设数据低秩的情况下，使用矩阵补全可以估计缺失数据的值，得到满足约束条件情况下最接近目标矩阵的结果矩阵。然而，在加入非高斯噪声的情况下，目前大部分矩阵补全算法的鲁棒性并不理想。为了增加矩阵补全算法的鲁棒性并避免算法过拟合，讨论了几种较为经典的矩阵补全算法，并提出了一种新的鲁棒性矩阵补全方法。该算法可以识别异常值的位置并用近似数据替换异常数据，降低异常值对算法的影响，增加精确度。模拟数据和真实数据的实验结果均显示，该算法在处理数据被高斯噪声毁坏的情况下有较好的鲁棒性和准确性。

关键词: 矩阵补全, 低秩矩阵恢复, 异常值, 鲁棒性