Statistical Nearest Neighbors for Image Denoising

Non-local-means image denoising is based on processing a set of neighbors for a given reference patch. few nearest neighbors (NN) can be used to limit the computational burden of the algorithm. Resorting to a toy problem, we show analytically that sampling neighbors with the NN approach introduces a bias in the denoised patch. We propose a different neighbors' collection criterion to alleviate this issue, which we name statistical NN (SNN). Our approach outperforms the traditional one in case of both white and colored noise: fewer SNNs can be used to generate images of superior quality, at a lower computational cost. A detailed investigation of our toy problem explains the differences between NN and SNN from a grounded point of view. The intuition behind SNN is quite general, and it leads to image quality improvement also in the case of bilateral filtering. The MATLAB code to replicate the results presented in the paper is freely available.