At the beginning of the imaging pipeline, data is acquired in a physical process measuring a metric which represents the interaction of a given probe with a sample. The physics of these interactions can be modelled mathematically. To form an image the model has to then be inverted, which is a challenging tasks due its ill-posedness, i.e. measurement errors leading to instabilities in the inversion or data being missing. Such so-called inverse problems are at the heart of almost any image formation process and their solution by modern regularization methods are the focus of the Research Unit at DESY. The goal of this unit is to strengthen the expertise in the mathematical field of inverse problems and to develop new modalities in specific domains by developing improved forward models, regularization methods and computational algorithms.