A new similarity measure for non-local means filtering of MRI images

• Non local means filters specifically designed and adapted for MRI noise are presented.
• The theoretical advantages of the associated similarity measures are discussed.
• Two closed-form expressions of the similarity measures for MRI data are derived.
• The practical relevance of the proposed measures is shown through numerical results.
• Noise types: Rice and non-central chi square with two degrees of freedom.

In this paper, the application of non-local means (NLM) filtering on MRI images is investigated. An essential component of any NLM-based algorithm is its similarity measure used to compare pixel intensities. Unfortunately, virtually all existing similarity measures used to denoise MRI images have been derived under the assumption of additive white Gaussian noise contamination. Since this assumption is known to fail at low values of signal-to-noise ratio (SNR), alternative formulations of these measures which take into account the correct (Rician) statistics of the noise are required. Accordingly, the main contribution of the present work is to introduce a new similarity measure for NLM filtering of MRI images, which is derived under bona fide statistical assumptions and proves to posses important theoretical advantages over alternative formulations. The utility and viability of the proposed method is demonstrated through a series of numerical experiments using both in silico and in vivo MRI data.