Inverse problems constitute an essential framework for approaching a large variety of issues in technical and medical domains. They are used to determine the underlying causes and structures on the basis of measurements or results. Examples include imaging techniques, where measurement data is used to produce an image of the inside of the body or the inside of a bridge pier. The challenge here is that most inverse problems have the vulnerability that even small perturbations in the data can trigger high oscillations in the solution. A research team at the Department of Mathematics, led by Elena Resmerita, is seeking to develop new and faster mathematical methods to find stable solutions to these problems.

“Instead of relying almost exclusively on the classic Euclidean distance between data points, as has been the case up to now, we want to use more sophisticated distance measures. These innovative mathematical tools allow us to target specific desired properties of solutions,” Elena Resmerita explains.
The aim of the project is to develop and analyse accelerated versions of several iterative methods based on such distance-like functions, both theoretically and computationally, and to compare them with well-established methods. “We are looking at a variety of fields of application and also want to investigate interesting links to machine learning and image processing,” says Elena Resmerita.
The project entitled ‘Distance-like based accelerated regularization methods’ is funded by the Austrian Science Fund FWF.
Der Beitrag Faster mathematical methods for stable technical solutions erschien zuerst auf University of Klagenfurt.