Contaminated Images Recovery by Implementing Non-negative Matrix Factorisation

TL;DR

This paper evaluates the robustness of various non-negative matrix factorisation algorithms for recovering contaminated images, highlighting their convergence behavior and robustness on face image datasets.

Contribution

The study provides a theoretical and experimental comparison of traditional NMF, HCNMF, and L2,1-NMF algorithms in the context of corrupted image data recovery.

Findings

Different algorithms require varying iterations to converge.

Final models often fail to converge within set iteration limits due to computational costs.

Experimental results demonstrate some robustness of the algorithms despite convergence issues.

Abstract

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.