Quantitative Susceptibility Mapping by Regulating the Field to Source Inverse Problem with a Sparse Prior Derived from the Maxwell Equation: Validation and Application to Brain

Jing Liu¹, Tian Liu², Ludovic de Rochefort³, Ildar Khalidov¹, Martin Prince¹, Yi Wang^1,2

Quantitative susceptibility mapping (QSM) is a promising technique for quantifying endogenous and exogenous susceptibility contrasts. The problem of deriving QSM from the measured field is under-determined and can be solved by optimization minimization programming. The prior information of the MR image magnitude can be used for promoting the sparsity of the minimization problem. The proposed method was validated by phantom experiments with high accuracy and good image quality. Brain susceptibility mapping provides good visualization as well as valuable quantification of iron accumulation in the brain.