Morphology enabled dipole inversion for quantitative susceptibility mapping using structural consistency between the magnitude image and the susceptibility map

► We present a dipole inversion for quantitative susceptibility mapping (QSM). ► The structural consistency between anatomy and susceptibility is used for inversion. ► We implement the structural consistency in the L1- and L2-norm minimization. ► The L1-norm is superior to the L2-norm for QSM accuracy and quality. ► High quality QSM is feasible for imaging brain structures and hemorrhages.