Inverse problems arise in a variety of physical problems, such as medium scattering, tomography, seismology and medical imaging just to name a few. In these problems only the effect, but not the cause is measured, and one has to recover (i.e. invert) the original cause. However, the naive inversion is often not unique valued or extremely unstable against observational noise. Powerful regularization methods are needed that incorporate prior information in the image. I am interested in a theoretical framework for inverse problems in general (exploring synergies between different imaging problems such as VLBI imaging and magnetic resonance imaging), and sparsity promoting regularization methods in particular. Recently we started to investigate methods based on neural networks. In a current project, we investigate synergies between the VLBI imaging and the Solar Orbiter mission.