# Leon Bungert

## Leon Bungert, M. Sc.

- Organization: Department of Mathematics
- Working group: Chair of Applied Mathematics (Inverse Problems) (Prof. Dr. Burger)
- Phone number: +49 9131 85-67206
- Fax number: +49 9131 85-67225
- Email: leon.bungert@fau.de
- Address:

Cauerstr. 11

91058 ErlangenRoom 04.331

### 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

**Asymptotic Profiles of Nonlinear Homogeneous Evolution Equations of Gradient Flow Type**

(2019)

URL: https://arxiv.org/abs/1906.09856
, :**Solution paths of variational regularization methods for inverse problems**

In:**Inverse Problems**(2019)

ISSN: 0266-5611

DOI: 10.1088/1361-6420/ab1d71

URL: https://arxiv.org/abs/1808.01783
, :**Computing Nonlinear Eigenfunctions via Gradient Flow Extinction**

SSVM 2019 (Hofgeismar, 30-06-2019 - 04-07-2019)

DOI: 10.1007/978-3-030-22368-7_23

URL: https://arxiv.org/abs/1902.10414
, , :

**Blind image fusion for hyperspectral imaging with the directional total variation**

In:**Inverse Problems**34 (2018)

ISSN: 0266-5611

DOI: 10.1088/1361-6420/aaaf63
, , , , , :**Robust Blind Image Fusion for Misaligned Hyperspectral Imaging Data**

In:**Proceedings in Applied Mathematics and Mechanics**18 (2018), p. 1 - 2

ISSN: 1617-7061

DOI: 10.1002/pamm.201800033
, , :**Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem**

In:**Computing and Visualization in Science**(2018)

ISSN: 1432-9360

DOI: 10.1007/s00791-018-0291-4

URL: https://link.springer.com/article/10.1007%2Fs00791-018-0291-4
, , :

### 2016

**A Discontinuous Galerkin Method for the Subjective Surfaces Problem**

In:**Journal of Mathematical Imaging and Vision**(2016), p. in press

ISSN: 1573-7683

DOI: 10.1007/s10851-016-0695-z
, , :