Magnetic resonance imaging allows us to take a look inside the body, but tends to be very slow. The algorithms currently used require a large amount of measurement data in order to generate images. As Barbara Kaltenbacher explains, significant progress has already been made: “Mathematical contributions to signal generation, image construction and motion compensation have already led to a reduction in scanning time and improved image quality. All of this has increased the diagnostic benefit.” Researchers involved in the special research area “Mathematics of Reconstruction in Dynamical and Active Models” are now looking to further refine these methods.

The researchers will use mathematics to model the entire process – from taking measurements to reconstructing the image. “At present, we still face limitations due to movement, incomplete data or noise sensitivity. We want to overcome these by means of jointly optimized and practically implementable measurement and reconstruction protocols,” Barbara Kaltenbacher continues.

Barbara Kaltenbacher goes on to explain that numerous areas of mathematics research are involved in achieving these objectives: “We need a broad perspective that optimizes innovations in calculus of variations, mathematical optimization, inverse problems, data science and MRI techniques.” Thanks to Barbara Kaltenbacher’s working group, the University of Klagenfurt can contribute extensive expertise in the field of inverse problems. These problems involve determining the causes of effects: For example, by measuring the distribution of tension on the surface of the body, it is possible to draw conclusions about the nature of the tissue in the body. Solving these types of problems often requires a lot of computing time. Barbara Kaltenbacher’s research focuses on developing new mathematical problem-solving methods that are faster and work better.

The special research area “Mathematics of Reconstruction in Dynamical and Active Models” is coordinated by the University of Graz. Alongside researchers from the University of Klagenfurt, researchers from the Vienna University of Technology and the Graz University of Technology are also involved.