On Nearest Neighbors in Non Local Means Denoising

TL;DR

This paper analyzes the bias introduced by using a limited number of nearest neighbors in Non-Local Means denoising and proposes a new statistical neighbor selection method that improves image quality and reduces computational cost.

Contribution

It introduces the Statistical NN (SNN) criterion, reducing bias and enhancing denoising performance over traditional nearest neighbor methods.

Findings

SNN outperforms traditional NN in denoising quality.

Fewer SNNs are needed for better results.

The method reduces computational cost.

Abstract

To denoise a reference patch, the Non-Local-Means denoising filter processes a set of neighbor patches. Few Nearest Neighbors (NN) are used to limit the computational burden of the algorithm. Here here we show analytically that the NN approach introduces a bias in the denoised patch, and we propose a different neighbors' collection criterion, named Statistical NN (SNN), to alleviate this issue. Our approach outperforms the traditional one in case of both white and colored noise: fewer SNNs generate images of higher quality, at a lower computational cost.