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

机译：MRI图像非局部均值滤波的新相似性度量

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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.
机译：本文研究了非局部均值（NLM）滤波在MRI图像上的应用。任何基于NLM的算法的基本组成部分是其相似性度量，用于比较像素强度。不幸的是，实际上所有现有的用于去噪MRI图像的相似性度量都是在假定加性高斯白噪声污染的前提下得出的。由于已知该假设在信噪比（SNR）值较低时会失败，因此需要这些措施的替代公式，并考虑到噪声的正确（Rician）统计量。因此，本工作的主要贡献是引入了一种新的用于MRI图像的NLM滤波的相似性度量，该度量是在善意的统计假设下得出的，并被证明具有比其他公式更重要的理论优势。通过使用计算机模拟和体内MRI数据进行的一系列数值实验，证明了该方法的实用性和可行性。

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