# Contaminated Images Recovery by Implementing Non-negative Matrix Factorisation

arXiv: https://arxiv.org/abs/2211.04247 · HTML: https://mlsanity.com/paper/2211.04247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 4 of 4)

- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Truncated Cauchy Non-negative Matrix Factorization](https://mlsanity.com/paper/1906.00495/) (2019)
- [VC-Net: Deep Volume-Composition Networks for Segmentation and Visualization of Highly Sparse and Noisy Image Data](https://mlsanity.com/paper/2009.06184/) (2020)
- [Analysis of the robustness of NMF algorithms](https://mlsanity.com/paper/2106.02213/) (2021)

## Abstract (arXiv)

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.