Combined Background Field Removal and Reconstruction for Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) is an emerging Magnetic Resonance Imaging (MRI) technique that provides in-vivo measurements of the magnetic susceptibility of, e.g., brain tissue. In practice, QSM requires solving a series of challenging inverse problem. Here, we will address two important steps, the removal of the background field, which is caused by sources outside the Region of Interest (ROI), and secondly, the reconstruction of dipole sources. In the recent past both problems have received attention, however, despite a large interdependence, each of it has been treated separately. We propose a new method that makes use of synergy effects by combining both steps. We demonstrate with numerical experiments that a combined treatment provides a better reconstruction of dipole sources close to the boundary of the ROI.