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Tomography refers to imaging methods where one attempts to recover the internal structure of a physical body from non-invasive boundary measurements. The most famous example is X-ray tomography used in hospitals. The mathematics of inverse problems focuses on extracting information from indirect data, and tomography is a central research topic in the field. Recently, machine learning has offered new data-driven possibilities for image reconstruction. Some of the results using, for example, the “U-net” are truly stunning. However, they are largely “black boxes,” and especially in medical imaging there is a great need for interpretability. This talk presents some ideas on using traditional inverse problems mathematics for calculating nonlinear features that are then used as inputs for machine learning. This way one could increase interpretability, reduce the size of networks needed for learning, allow the use of smaller training data sets, and increasing the robustness of the network (the image formation tasks in ill-posed inverse problems of tomography are very sensitive to noise).

Speaker: Samuli Siltanen

Affiliation: Professor of Industrial Mathematics, University of Helsinki