A Bayesian Hierarchical Model for Noise Reduction in Low-field Magnetic Resonance Imaging

In current magnetic resonance imaging (“MRI”) systems, low-field MRI has the advantage of low cost and open. The signal-to-noise ratio (“SNR”) obtained, however, is relatively low. This study thus aims at developing a Bayesian multi-stage hierarchical model with an outlier-detection ability, through the use of a heavy-tailed prior that can be used to reduce the effects of noise introduced. Since the introduction of Bayesian image processing, it has been actively applied to positron emission tomography (“PET”) studies, but the application in MRI has been limited. In particular, there has been no publication on its implementation for low-field MRI which should be of the present interest. The most desirable feature of this Bayesian approach is the ability to incorporate general a priori knowledge into the model. This helps improve the image quality when the SNR is low. Further, a Bayesian multi-stage hierarchical model improves the conventional Bayesian estimation with a member of the heavy-tailed family. The use of a heavy-tailed prior in the hierarchical model will increase the degree of complexity, however, with scale mixtures of normal (“SMN”), the implementation is made easier. This advantage is particularly significant and useful for low-field MRI. The proposed model will also be compared to the conventional Bayesian estimation as well as other members of the heavy-tailed distribution family.