Pure model-based approaches are today often insufficient for solving complex inverse problems in imaging. At the same time, we witness the tremendous success of data-based methodologies, in particular, deep neural networks for such problems. However, pure deep learning approaches often neglect known and valuable information from physics.

In this talk, we will provide an introduction to this problem complex and then discuss a general conceptual approach to inverse problems in imaging, which combines deep learning and physics. This hybrid approach is based on shearlet-based sparse regularization and deep learning and is guided by a microlocal analysis viewpoint to pay particular attention to the singularity structures of the data. Finally, we will present several applications such as tomographic reconstruction and show that our approach outperforms previous methodologies, including methods entirely based on deep learning.