A common limitation of MRI are the comparably long measurement times. In this project, we aim to address this problem by developing sophisticated image reconstruction methods taking into account our prior knowledge about the expected structure of MRI images. Moreover, we are interested in the development of robust reconstruction methods that take into account system imperfections such as the inhomogeneity of the main magnetic field. For fast imaging sequences with long readouts, neglecting such imperfections leads to visible artifacts corrupting the image. Incorporating imperfections into the reconstruction thus opens up the door to use fast imaging sequences and thus allows to reduce the scan time or improve the resolution.