Fast and accurate reconstruction for susceptibility source separation in QSM

We investigate fast and accurate reconstruction methods for susceptibility source separation (S3) in quantitative susceptibility mapping (QSM). S3 separates positive and negative susceptibility sources within a voxel utilizing signal relaxation (R2') for dipole inversion. We propose new primal-dual (PD) methods for S3 and compare them with the alternating Gauss-Newton conjugate gradient (A-GNCG). A-GNCG alters the energy functional, and furthermore its convergence is not guaranteed. In contrast, the proposed PD methods are exact and have convergence guarantees. Validation on a simulated phantom and in-vivo data shows that the PD methods converge faster with better accuracies.