Our research activities

Our main research activities

The classic regularisation theory is based on the assumption that the searched-for quantity is stationary during the data acquisition. However, in many applications from medicine to non-destructive testing, this assumption is not fulfilled, for example when investigating cross-scale structural changes of materials under load experiments or moving liquid fronts in porous media.

Applying the standard techniques from the literature provides a solution with low spatial or temporal resolution and introduces motion artefacts which impede a reliable diagnosis. Therefore, our research strives after developing a comprehensive regularization theory for dynamic inverse problems, new mathematical models with a specific treatment of the dynamics and new inversion schemes.

Developing new imaging modalities and new fields of applications necessitates novel approaches in mathematical modelling, data processing and image reconstruction. A special focus of our group lies in this respect on computerized tomography and microscopy.

The relentless progress in imaging technology and the exploitation of new fields of application require new mathematical models and numerical solution methods. The special focus of our group lies on classical modalities like computerized tomography or magnetic resonance imaging as well as on novel tomographic methods like magnetic particle imaging.


In order to extract features and properties of the studied medium, the reconstruction results are typically subject to further processing steps. Since an ever-increasing amount of data arises in modern applications, special algorithms are required to extract the desired information in an efficient and stable way. In this context, it is desirable to obtain this information directly from the data, i.e. in the form of a feature reconstruction.

Classical solution schemes for inverse problems are based on mathematical models which describe the link between data and searched-for quantity. For many classes of such model-based reconstruction methods, their convergence properties are well understood.

In novel, data-driven reconstruction methods, the sought-for quantity is determined by the evaluation of a neural network whose parameters have previously been trained on suitable test data. Thus, redundancies, structures and features in the test data can be identified and used for the solution step without explicit modeling.

A major difficulty of purely data-driven approaches is to establish a control over the output. Therefore, we investigate in the project iDeLIVER the combination of model-based and data-driven methods in order to enable a high acceleration of the reconstruction step without compromising the e.g. diagnostic validity.

Current research projects and cooperations

Project ccordinator: Prof. Dr. Bernadette Hahn-Rigaud

Project period: 2020-2023

Funding institution: Federal Ministry of Education and Research (BMBF)

Project description:

The project examines the use and further development of machine learning methods for MR image reconstruction and for the classification of liver lesions.
Based on a comparison model and data-driven image reconstruction methods, these are to be systematically linked in order to enable high acceleration without sacrificing diagnostic value. In addition to the design of suitable networks, research should also be carried out to determine whether metadata (e.g. age of the patient) can be incorporated into the reconstruction. Furthermore, suitable classification algorithms on an image basis are to be developed and the potential of direct classification on the raw data is to be explored. In the long term, intelligent MR diagnostics can significantly increase the efficiency of use of MR hardware, guarantee better patient care and set new impulses in medical technology.

Involved research and application partners within the project:

  • Prof. Dr. Bernadette Hahn-Rigaud, Chair of Optimization and inverse Problems, University of Stuttgart
  • Prof. Dr. Alfio Borzì, Chair of Mathematics IX, Scientific Computing, JMU Würzburg
  • Prof. Dr. Andreas Maier, Pattern Recognition Lab, FAU Erlangen-Nürnberg
  • Prof. Dr. Herbert Köstler und Prof. Dr. Tobias Wech, Experimental Radiology, Universitätsklinikum Würzburg
  • Prof. Dr. Thorsten Bley, Department of Diagnostic and Interventional Radiology, Universitätsklinikum Würzburg
  • Dr. Moritz Berger, Siemens Healthcare GmbH, Erlangen
  • Prof. Dr. Karsten König und Dr. Andreas Schindele, JenLab GmbH, Berlin

Research Assistant (University of Stuttgart):
MSc. Mathias Feinler

Website iDeLIVER

Project period: 2020-2023

Funding institution: German Research Foundation (DFG)

Project description:

The project deals with three dynamic aspects in MPI (concentration dynamic, magnetic field dynamic and particle magnetizing dynamic) which lead to a numerous number of dynamic inverse problems. The goal is to develop reconstruction methods which explicitly include the dynamic behaviour.

Involved research partners within the project:

  • Prof. Dr. Bernadette Hahn-Rigaud, University of Stuttgart
  • Dr. Tobias Kluth, Zentrum für Technomathematik, University of Bremen

Research Assistant (University of Stuttgart):
MSc. Marius Nitzsche

Project period: 2017-2021

Funding institution: German Research Foundation (DFG)

Project description:

Das Projekt behandelt Bildgebungsverfahren mit sich bewegendem Objekt. Die zusätzliche Zeitdimension verändert den Grad der Schlecht-Gestelltheit, die räumliche Auflösung oder führt zu unvollständigen Daten. Diese Aspekte sollen analysiert und geeignete Regularisierungsverfahren entwickelt werden.

Research Assistant (University of Stuttgart):
MSc. Melina-Loren Kienle Garrido

We currently hold external cooperations ie. with the following institutions:

  • University of the Saarland, Germany
  • University of Bremen, Germany
  • Julius-Maximilians-University Würzburg, Germany
  • Universitätsklinikum Würzburg, Germany
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
  • Fraunhofer Institute IIS, Erlangen, Germany
  • IzfP Tufts University, USA
This image shows Bernadette  Hahn-Rigaud

Bernadette Hahn-Rigaud

Prof. Dr.

Chairholder OIP

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