Models used in inverse problems are never complete and even more importantly such models, perhaps optimal in given function spaces, hardly cover realistic inputs stemming from only a subset of the space of the unknowns, which however is unknown. Hence, data driven corrections to analytical models can compensate for both shortcomings. We analyze mathematically neural networks for solving almost trivial inverse problems and discuss data driven updates to the analytical model of magnetic particle imaging.

This presentation is part of Minisymposium “MS72 - Inverse problems with imperfect forward models (2 parts)”
organized by: Yury Korolev (University of Cambridge) , Martin Burger (University of Muenster) .

Authors:

Peter Maass (University of Bremen)

Tobias Kluth (University of Bremen)

Hannes Albers (University of Bremen)

Keywords:

deep learning, image reconstruction, inverse problems