Robust Quantitative Susceptibility Mapping via Approximate Message Passing with Parameter Estimation

Abstract

We propose a robust Bayesian approach with built-in parameter estimation for quantitative susceptibility mapping (QSM). From a Bayesian perspective, wavelet coefficients of the susceptibility map are modeled by Laplace distribution. Noise is modeled by a two-component Gaussian-mixture distribution, where the second component is reserved to model the noise outliers. The susceptibility map and distribution parameters are jointly recovered using approximate message passing (AMP). The proposed approach achieves better performance in challenging cases of brain hemorrhage and calcification. It automatically estimates the parameters, which avoids subjective bias from the usual visual-tuning step of in vivo reconstruction.