The research group of Prof. Hesser focuses on the field of inverse problems. To mention a few, image reconstruction, segmentation, classification etc. play a vital role for clinical decision systems (CDS) or therapy support systems (TSS) but also for preclinical research. Deep learning changed the field substantially by learning the model or the prior distribution via measured or simulated data. Also issues like uncertainty and causal inference are of high importance. We are focusing on basic mathematical tools, their properties and how they can be applied for selected applications in computational medicine.