Theoretical Foundations of Uncertainty-Aware Deep Learning for Inverse Problems

• Applicants: Professor Dr. Martin Burger; Professor Dr. Michael Möller
• Subject Area: Mathematics ; Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 464101190

This project continues the development of theoretically founded deep learning methods for inverse problems with a particular focus on the treatment of uncertainties. A key issue in learning based methods is the fact that training data may be different from typical data arising later in applications, e.g. since they are simulated data. We will develop a suitable mathematical theory of such uncertainties in the training data and methods to robustify the learning process against those. Moreover, we will develop novel methods to deal with cases where an insufficient number of training data for fully supervised learning is available. A second objective of the project is to develop methods to quantify uncertainty in deep learning methods for inverse problems. This is to be achieved in a Bayesian setting by producing samples, for which we develop suitable schemes in a diffusion framework. Moreover, we develop novel approaches to sample the diversity of possible solutions reliably explaining the measured data. The final step is to develop uncertainty-aware deep learning towards large scale applications. For this sake we target state-of-the art imaging techniques with X-rays and optical frequencies, including the problem of phase retrieval.

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