Containminated Images Recovery by Implementing Non-negative Matrix Factorisation

Non-negative matrix factorisation (NMF) has been widely used to address the problem of corrupted data in images. The standard NMF algorithm minimises the Euclidean distance between the data matrix and the factorised approximation. Although this method has demonstrated good results, because it employs the squared error of each data point, the standard NMF algorithm is sensitive to outliers. In this paper, we theoretically analyse the robustness of the standard NMF, HCNMF and L2,1-NMF algorithms, and implement sets of experiments to show the robustness on real datasets, namely ORL and Extended YaleB. Our work demonstrates that different amounts of iterations are required for each algorithm to converge. Given the high computational complexity of these algorithms, our final models such as HCNMF and L2,1-NMF model do not successfully converge within the iteration parameters of this paper. Nevertheless, the experimental results still demonstrate the robustness of the aforementioned algorithms to some extent.