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Eirik Østmo / Torger Grytå

VI seminar 2021 #6 - Deep Learning meets Modeling: Taking the Best out of Both Worlds

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Presenter: Gitta Kutyniok, Bavarian AI Chair for "Mathematical Foundations of Artificial Intelligence" in the institute of mathematics at the Ludwig Maximilian University of Munich and adjunct professor at Visual Intelligence at UiT

Gitta Kutyniok

Abstract: Pure model-based approaches are today often insufficient for solving complex inverse problems in medical imaging. At the same time, we witness the tremendous success of data-based methodologies, in particular, deep neural networks for such problems. However, pure deep learning approaches often neglect known and valuable information from the modeling world and are not interpretable.

In this talk, we will develop a conceptual approach by combining the model-based method of sparse regularization by shearlets with the data-driven method of deep learning. Our solvers are guided by a microlocal analysis viewpoint to pay particular attention to the singularity structures of the data. Focussing then on the inverse problem of (limited-angle) computed tomography, we will show that our algorithms significantly outperform previous methodologies, including methods entirely based on deep learning. Finally, we will also briefly touch upon the issue of how to interpret such approaches.

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