A novel method for dipole inversion in QSM with reweighted L2-norm using distribution specification

Dipole inversion is the final step of the QSM algorithm. In this step, the zero cone surface in the dipole kernel makes the field-to-susceptibility inverse problem ill-posed. Current solutions are mostly based on the Bayesian approach. Compared to the L1-norm, which has been used in previous techniques, the L2-norm converges faster. Therefore, we propose to employ a reweighted L2-norm using weights that are renewed after each iteration such that the multiplication of weights and the susceptibility gradient satisfy the Gaussian distribution. This is considered to be consistent with the a priori knowledge of the L2-norm. Results of phantom and in vivo experiments demonstrate that this novel Distribution Specified Dipole Inversion (DSDI) method enhances the quality of QSM reconstruction image and shortens calculation time remarkably.