Nonlinear formulation of the magnetic field to source relationship for robust quantitative susceptibility mapping

Quantitative susceptibility mapping (QSM) opens the door for measuring tissue magnetic susceptibility properties that may be important biomarkers, and QSM is becoming an increasingly active area of scientific and clinical investigations. In practical applications, there are sources of errors for QSM including noise, phase unwrapping failures, and signal model inaccuracy. To improve the robustness of QSM quality, we propose a nonlinear data fidelity term for frequency map estimation and dipole inversion to reduce noise and effects of phase unwrapping failures, and a method for model error reduction through iterative tuning. Compared with the previous phase based linear QSM method, this nonlinear QSM method reduced salt and pepper noise or checkerboard pattern in high susceptibility regions in healthy subjects and markedly reduced artifacts in patients with intracerebral hemorrhages.