A Quantitative Theory of the Non-Local Means Algorithm

Noise filtering is a common step in image processing, and is particularly effective in improving the subjective quality of images. A number of techniques have been developed, many of which concentrate on the problem of removing noise without damaging small structures, such as edges. One recent approach demonstrating empirical merit is Non-Local Means (NLM). However, an understanding of the statistical basis of NLM is required before it can be used in quantitative image analysis. In this paper we invertigate this basis in order to understand the conditions required for the use of NLM, testing the theory on simulated data and MR images of the normal brain.