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

The magnetic susceptibility of tissue can be determined in gradient echo MRI by deconvolving the local magnetic field with the magnetic field generated by a unit dipole. This Quantitative Susceptibility Mapping (QSM) problem is unfortunately ill-posed. By transforming the problem to the Fourier domain, the susceptibility appears to be undersampled only at points where the dipole kernel is zero, suggesting that a modest amount of additional information may be sufficient for uniquely resolving susceptibility. A Morphology Enabled Dipole Inversion (MEDI) approach is developed that exploits the structural consistency between the susceptibility map and the magnitude image reconstructed from the same gradient echo MRI. Specifically, voxels that are part of edges in the susceptibility map but not in the edges of the magnitude image are considered to be sparse. In this approach an L ₁ norm minimization is used to express this sparsity property. Numerical simulations and phantom experiments are performed to demonstrate the superiority of this L ₁ minimization approach over the previous L ₂ minimization method. Preliminary brain imaging results in healthy subjects and in patients with intracerebral hemorrhages illustrate that QSM is feasible in practice.