Deep-Learning Based Regularization of Inverse Problems

• Applicants: Professor Dr. Martin Burger; Professorin Dr. Gitta Kutyniok
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 464101359

Deep learning has attracted enormous attention in many fields like image processing and consequently it receives growing interest as a method to regularize inverse problems. Despite its great potential, the development of methods and in particular the understanding of deep networks in this respect is still in its infancy. We hence want to advance the construction of deep-learning based regularizers for ill-posed inverse problems and their theoretical foundations.Particular goals are the development of robust and interpretable results, which enforce to develop novel concepts of robustness and interpretability in this setup. The theoretical developments will be accompanied by extensive computational tests and the development of measures and benchmark problems for fair comparison of different approaches.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2298: Theoretical Foundations of Deep Learning