Non-Local means est un algorithme de d\'ebruitage local (Non-Local means is a local image denoising algorithm)

TL;DR

This paper demonstrates that the Non-Local Means (NLM) denoising algorithm is inherently local, with optimal performance achieved using a small search window, due to noise disrupting patch similarity measures.

Contribution

The study provides experimental evidence that NLM's effectiveness depends on a small locality constraint, challenging the view that NLM captures global image similarities reliably.

Findings

Bias increases with larger search zones due to noise disrupting patch similarity

Optimal search radius for NLM is around 3 to 4 pixels

NLM is fundamentally a local denoising method

Abstract

The Non-Local Means (NLM) image denoising algorithm pushed the limits of denoising. But it introduced a new paradigm, according to which one could capture the similarity of images with the NLM weights. We show that, contrary to the prevailing opinion, the NLM weights do not allow to get a reliable measure of the similarity in a noisy image, unless one add a locality constraint. As an image denoising method, the Non-Local Means prove to be local. Some works had already pointed out that to get the best denoising performances with the NLM algorithm, one should run it locally. But no general conclusion has been yet proposed and the only explanation that was proposed to justify the experimental results is not sufficient. Our study based on experimental evidence proves that, on average on natural images, the bias of the NLM estimator is an increasing function of the radius of the similarity searching zone. The reason for this phenomenon is that noise disrupts the order of similarity between patches. Hence the mean squared error between the original image and the NLM estimation, which is the sum of the bias, the variance and the covariance of the estimator, has an absolute minimum for a disk of radius 3 to 4 pixels.