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The acquisition of MRI images offers a trade-off in terms of acquisitiontime, spatial/temporal resolution and signal-to-noise ratio (SNR). Thus, forinstance, increasing the time efficiency of MRI often comes at the expense ofreduced SNR. This, in turn, necessitates the use of post-processing tools fornoise rejection, which makes image de-noising an indispensable component ofcomputer assistance diagnosis. In the field of MRI, a multitude of imagede-noising methods have been proposed hitherto. In this paper, the applicationof a particular class of de-noising algorithms - known as non-local mean (NLM)filters - is investigated. Such filters have been recently applied for MRI dataenhancement and they have been shown to provide more accurate results ascompared to many alternative de-noising algorithms. Unfortunately, virtuallyall existing methods for NLM filtering have been derived under the assumptionof additive white Gaussian (AWG) noise contamination. Since this assumption isknown to fail at low values of SNR, an alternative formulation of NLM filteringis required, which would take into consideration the correct Rician statisticsof MRI noise. Accordingly, the contribution of the present paper is two-fold.First, it points out some principal disadvantages of the earlier methods of NLMfiltering of MRI images and suggests means to rectify them. Second, the paperintroduces a new similarity measure for NLM filtering of MRI Images, which isderived under bona fide statistical assumptions and results in more accuratereconstruction of MR scans as compared to alternative NLM approaches. Finally,the utility and viability of the proposed method is demonstrated through aseries of numerical experiments using both in silico and in vivo MRI data.

A New Similarity Measure for Non-Local Means Filtering of MRI Images