1. A method for performing quantitative susceptibility mapping using a magnetic resonance imaging (MRI) system, the steps of the method comprising: a) acquiring data from a subject using the MRI system; b) reconstructing phase images from the acquired data; c) computing at least one initial estimate of a susceptibility map based on the reconstructed phase images; d) determining a first regularization parameter based on the at least one initial estimate of the susceptibility map; and e) iteratively reconstructing a susceptibility map using an l 1 -minimization that comprises minimizing an objective function that includes the first regularization parameter and a second regularization parameter that is determined based on iterative updates of the susceptibility map.