# Pruned non-local means

## TL;DR

This paper introduces a pruning technique for Non-Local Means denoising that improves performance by rejecting low-weight neighboring pixels, especially near edges, with optimal threshold tuning via Stein's estimator.

## Contribution

It proposes a novel pruning method for NLM that enhances denoising quality and provides a way to optimally select the threshold using Stein's unbiased estimator.

## Key findings

- Improved denoising performance over standard NLM.
- Effective near edges and corners.
- Threshold tuning with minimal computational overhead.

## Abstract

In Non-Local Means (NLM), each pixel is denoised by performing a weighted averaging of its neighboring pixels, where the weights are computed using image patches. We demonstrate that the denoising performance of NLM can be improved by pruning the neighboring pixels, namely, by rejecting neighboring pixels whose weights are below a certain threshold $\lambda$. While pruning can potentially reduce pixel averaging in uniform-intensity regions, we demonstrate that there is generally an overall improvement in the denoising performance. In particular, the improvement comes from pixels situated close to edges and corners. The success of the proposed method strongly depends on the choice of the global threshold $\lambda$, which in turn depends on the noise level and the image characteristics. We show how Stein's unbiased estimator of the mean-squared error can be used to optimally tune $\lambda$, at a marginal computational overhead. We present some representative denoising results to demonstrate the superior performance of the proposed method over NLM and its variants.