Non-local Sigma Filter

Abstract

This paper proposes a non-local modification of well-known sigma filter, Nonlocal Sigma filter (NSF), intended to suppress additive white Gaussian noise from images. Similarly to the Nonlocal Mean Filter (NLM), every output pixel value is computed as a nonlocal weighted average of pixels coming from similar patches to the patch around the current pixel. The main difference between the proposed NSF and NLM is in the following: there are pixels in NSF not used in a weighted averaging (if the difference between them and the central pixel value is above a predefined threshold value, and if the distance between patch neighborhood and the central patch neighborhood is greater than a second threshold value). The weights used to estimate the output pixel depend on the patch size as well as on a distance between considered and reference patches. The proposed filter is compared to its counter-parts, namely, the conventional sigma filter and the NLM filter. It is shown that NSF outperforms both of them in PSNR and visual quality metrics values, PSNR-HVS-M and MSSIM. In this paper, a novel filtering quality criterion that takes into account distortions introduced into processed images due to denoising is proposed. It is demonstrated that, according to this criterion, NSF has similar edge-detail preservation property as the conventional sigma filter but has better noise suppression ability.