Using Prior Knowledge for the Solution of Ill-Posed Inverse Problems in X-Ray Microscopy

Supervisors: Prof. Christian Schroer (DESY, UHH), Prof. Tobias Knopp (TUHH, UKE)

The interpretation of most experimental data in X-ray microscopy requires solving an inverse problem, i. e., finding the physical properties of a sample from a more or less known model for the image formation. Solving such inverse problems is usually a challenging task since the underlying mathematical problem is ill-posed and in turn small perturbations in the measurement due to noise lead to large errors in the calculated solution of the inverse problem. To handle inverse problems, the underlying linear reconstruction problem has to be solved by applying prior knowledge. For instance it can be assumed that the solution is smooth or that it has minimal total variation. In the recent years, the classical solvers for inverse problems have been complemented by approaches that are based on machine learning. Based on large databases of typical images, the inverse imaging operator can be learned and efficiently evaluated. Within this project the goal is to implement, improve, and compare state-of-the art algorithms for the solution of the inverse problem in X-ray microscopy using real-world data. The algorithms will be benchmarked with respect to noise reduction and reconstruction speed. A major focus will be put on the investigation of artifacts that appear when the algorithms are applied to unusual but physically plausible data.