Structured model learning

This project is part of the special research area Mathematics of Reconstruction in Dynamical and Active Models, which is a joint research effort of four Universities at three different locations (Graz, Vienna and Klagenfurt) in Austria.

The overall goal of the special research area is to develop new mathematical models and methods for imaging modalities such as magnetic resonance imaging (MRI). MRI is an important achievement in medical imaging that is heavily used in clinics world wide. A big advantage of MRI (compared, e.g., to computer tomography) is its capability to visualize differences between different types of soft tissue, as well as its versatility, allowing MRI to image not only tissue density, but for example also chemical properties of the tissue, blood flow or magnetic tissue properties. MRI, and in particular these advanced MRI protocols, however, require sophisticated mathematical models to create images from the data that is actually measured at the MR machine. Furthermore, a big challenge in MRI is that data acquisition is rather slow, which often prohibits the imaging of fast, dynamic processes.

The goal of the special research area is to significantly advance the imaging capabilities of MRI and similar modalities by developing a comprehensive mathematical and methodological framework to describe, control and optimize the data acquisition and image formation process. 

This comprises the development of new methods for optimized measurement protocols, parameter identification and the modeling of image data.

Within this special research area, the goal of our subproject Structured model learning is to develop and analyze a machine-learning framework that allows to augment approximately correct physical models with components that are learned from data. This is in particular important for MRI, where existing physical models that describe the measurement process are not always capable of modelling all involved processes sufficiently well.

Our project will provide new possibilities of learning physical models from data in a highly structured way. Within our project, we will answer question such as: How much data do I need to learn components of a model with a certain complexity? Is it possible to uniquely identify the underlying physics from the available data? How do I implement machine learning algorithms for model learning in a way that the correct model can be found?

By answering these questions, our project aims to contribute to a better understanding of the of different MR imaging protocols and, ultimately, to provide improved imaging techniques for medical diagnosis and therapy control.