Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## Deep Learning meets Modeling: Taking the Best out of Both Worlds

Prof. Dr. Gitta Kutyniok talk

**Date:** 07.10.19 **Time:** 16.15 - 17.45 **Room:** ETH HG G 19.2

Inverse problems in imaging such as denoising, recovery of missing data, or the inverse scattering problem appear in numerous applications. However, due to their increasing complexity, model-based methods are often today not sufficient anymore. 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 also currently still lack a profound theoretical understanding. In this talk, we will provide an introduction to this problem complex and then focus on the inverse problem of computed tomography, where one of the key issues is the limited angle problem. For this problem, we will demonstrate the success of hybrid approaches. We will develop a solver for this severely ill-posed inverse problem by combining the model-based method of sparse regularization by shearlets with the data-driven method of deep learning. Our approach is faithful in the sense that we only learn the part which cannot be handled by model-based methods, while applying the theoretically controllable sparse regularization technique to all other parts. We further show that our algorithm significantly outperforms previous methodologies, including methods entirely based on deep learning. Finally, we will discuss how similar ideas can also be used to solve related problems such as detection of wavefront sets.