Abstract: Quantitative Susceptibility Mapping (QSM) is a MRI technique that allows to image magnetic properties of tissue. QSM is applied increasingly, for example, in neuroscience, where iron concentration serves as a biomarker of certain neurological diseases. While the tissue’s susceptibility cannot be measured directly it can be reconstructed by solving a highly ill-posed inverse problem. In this talk, we will present joint methods for QSM reconstruction as well as the related subproblem of background field removal.