# Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means

arXiv: https://arxiv.org/abs/1403.2482 · HTML: https://mlsanity.com/paper/1403.2482/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2014.

## Built on by (most cited first, 1 of 1)

- [Low rank prior and l0 norm to remove impulse noise in images](https://mlsanity.com/paper/2209.05234/) (2022)

## Abstract (arXiv)

We first establish a law of large numbers and a convergence theorem in distribution to show the rate of convergence of the non-local means filter for removing Gaussian noise. We then introduce the notion of degree of similarity to measure the role of similarity for the non-local means filter. Based on the convergence theorems, we propose a patch-based weighted means filter for removing impulse noise and its mixture with Gaussian noise by combining the essential idea of the trilateral filter and that of the non-local means filter. Our experiments show that our filter is competitive compared to recently proposed methods.