Combining imaging, physics and analysis for rheological experiments

This project addresses challenges arising in computerized tomography (CT) of rheological experiments which are due to the dynamic behaviour of the material under study. Since the CT-data acquisition takes a considerable amount of time, only a limited amount of data can be recorded for each state of the object resulting in severe artefacts in the reconstructed images. We therefore strive to develop appropriate reconstruction algorithms by combining data-driven techniques with a suited physical process. Ignoring the temporal correlation between the different states of the material under study in rheological experiments leads to reconstructed images with severe undersampling and/or motion artefacts. This can be encountered for by including suitable a priori information, for instance about the static structure of the specimen, which can be recorded via a high-resolution scan before the dynamic experiment starts. To this end, we focus in a first step on the characterization and estimation of the motion from large datasets guided by inconsistency detections in the data and the optical flow equation. Our subsequent goal is then to combine this derived information with reconstruction approaches, such as RESESOP or learned primal dual, able to handle imperfect models. Finally, we propose to enhance the quality of reconstruction and learning by considering the propagation of singularities, understood by microlocal analysis, and differentiating between features and artifacts.