A pull-push method for fast non-local means filtering

Abstract

Non-local means filtering (NLM), has garnered a large amount of interest in the image processing community due to its capability to exploit image patch self-similarity in order to effectively filter noisy images. However, the computational complexity of non-local means filtering is the product of three different factors; namely, O(NDK), where K is the number of filter kernel taps (e.g. search window size), D is the number of patch taps, and N is number of pixels. We propose a fast approximation of non-local means filtering using the multiscale methodology of the pull-push scattered data interpolation method. By using NLM with a small filter kernel to selectively propagate filtering results and noise variance estimates from fine to coarse scales and back, the process can be used to provide comparable filtering capability to brute force NLM but with algorithmic complexity that is linear in the number of image pixels and the patch comparison taps, O(ND). In practical application, we demonstrate its denoising capability is comparable to NLM with much larger filter kernels, but at a fraction of the computational cost.