论文标题
通过实施非负矩阵分解，受污染的图像恢复
Contaminated Images Recovery by Implementing Non-negative Matrix Factorisation
论文作者
论文摘要
非负矩阵分解（NMF）已广泛应用于损坏的图像数据问题。标准的NMF方法最大程度地减少了数据矩阵和分解近似之间的欧几里得距离。传统的NMF技术对离群值敏感，因为它利用了每个数据点的平方误差，尽管该方法已被证明有效。在这项研究中，我们从理论上研究了传统的NMF，HCNMF和L2,1-NMF算法的鲁棒性，并执行了一组实验集，以证明ORL和扩展的Yaleb数据集上的稳健性。我们的研究表明，每种算法都需要不同数量的迭代来收敛。由于这些方法的计算成本，我们的最终模型（例如HCNMF和L2,1-NMF模型）无法在本工作的迭代参数中收敛。但是，实验结果在某种程度上说明了上述技术的鲁棒性。
Non-negative matrix factorisation (NMF) has been extensively applied to the problem of corrupted image data. Standard NMF approach minimises Euclidean distance between data matrix and factorised approximation. The traditional NMF technique is sensitive to outliers since it utilises the squared error of each data point, despite the fact that this method has proven effective. In this study, we theoretically examine the robustness of the traditional NMF, HCNMF, and L2,1-NMF algorithms and execute sets of experiments to demonstrate the robustness on ORL and Extended YaleB datasets. Our research indicates that each algorithm requires a different number of iterations to converge. Due to the computational cost of these approaches, our final models, such as the HCNMF and L2,1-NMF model, fail to converge within the iteration parameters of this work. Nonetheless, the experimental results illustrate, to some extent, the robustness of the aforementioned techniques.
