# Low rank prior and l0 norm to remove impulse noise in images

arXiv: https://arxiv.org/abs/2209.05234 · HTML: https://mlsanity.com/paper/2209.05234/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 2 of 2)

- [Variational based Mixed Noise Removal with CNN Deep Learning Regularization](https://mlsanity.com/paper/1805.08094/) (2018)
- [Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means](https://mlsanity.com/paper/1403.2482/) (2014)

## Abstract (arXiv)

Patch-based low rank is an important prior assumption for image processing. Moreover, according to our calculation, the optimization of l0 norm corresponds to the maximum likelihood estimation under random-valued impulse noise. In this article, we thus combine exact rank and l0 norm for removing the noise. It is solved formally using the alternating direction method of multipliers (ADMM), with our previous patch-based weighted filter (PWMF) producing initial images. Since this model is not convex, we consider it as a Plug-and-Play ADMM, and do not discuss theoretical convergence properties. Experiments show that this method has very good performance, especially for weak or medium contrast images.