Dr. Leon Bungert

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Research Interests

My research primarily focuses on spectral theory of nonlinear operators. For instance, I examine how eigenvectors of these operators can be calculated and under which conditions one can decompose an arbitrary vector into eigenvectors.

What may sound abstract has numerous applications in pattern recognition as well in signal and image processing. For example, if you want to subdivide the network of your Facebook friends into peer groups, the optimal subdivision is described by the eigenvector of a nonlinear operator. Inner-mathematically, the study of nonlinear eigenproblems has interesting connections to the asymptotic behavior of partial differential equations or the solution of inverse problems.

My second research interest is image reconstruction using structural side-information. Within imaging one often differentiates between functional and structural imaging. The former typically allows to visualize information that is invisible to the human eye, such as infrared radiation. Structural imaging, in contrast, as the name suggests, is able to map spatial structures very precisely, as for example high-resolution cameras do. I am working on methods to combine the best of these two worlds, i.e. to fuse a functional image and a structural image into a functional image with a high spatial resolution. This is particularly challenging if the two images are not co-registered.

Résumé

• *1994 in Nürnberg
• Abitur, Ostendorfer Gymnasium Neumarkt i.d.OPf., 2012.
• Bachelor of Science in Mathematics with minor Theoretical Physics, FAU Erlangen, 2016.
• Master of Science in Mathematics with minor Computer Science, FAU Erlangen, 2017.
• Research Assistant and PhD Student at Institute for Applied Mathematics, WWU Münster, 04/2018 – 09/2018.
• Research Assistant and PhD Student at Chair for Applied Mathematics, FAU Erlangen, from 10/2018.

Projects

Publications