Anisotropic LMMSE denoising of MRI based on statistical tissue models

Linear Minimum Mean Squared Error Estimation (LMMSE) is a simple, yet powerful denoising technique within MRI. It is based on the computation of the mean and variance of the data being filtered according to a noise model assumed, which is usually accomplished by calculating local moments over squared neighborhoods. When these neighborhoods are centered in pixels corresponding to image contours, the estimation is not accurate due to the presence of two or more tissues with different statistical properties. We overcome this limitation by introducing an anisotropic LMMSE scheme: the gray levels of each tissue in the MRI volume are modeled as a Gamma-mixture, such that we can discriminate between the different matters to construct anisotropic neighborhoods containing only one kind of tissue. The potential of the Gamma distribution relies on its ability to fit both the Rician distribution traditionally used to model the noise in MRI and the non-central Chi noise found in modern parallel MRI systems.