Dr. Leon Bungert
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.
- *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.
Variational regularisation for inverse problems with imperfect forward operators and general noise models
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The infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
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Structural analysis of an $L$-infinity variational problem and relations to distance functions
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Robust Image Reconstruction with Misaligned Structural Information
Nonlinear Power Method for Computing Eigenvectors of Proximal Operators and Neural Networks
In: arXiv (2020)
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The lion in the attic – A resolution of the Borel–Kolmogorov paradox
Localization of Passive 3D-Coils as an Inverse Problem: Theoretical Analysis and a Numerical Method
In: IEEE Transactions on Magnetics (2020)
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Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
SSVM 2019 (Hofgeismar, 30-06-2019 - 04-07-2019)
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Solution paths of variational regularization methods for inverse problems
In: Inverse Problems (2019)
Nonlinear Spectral Decompositions by Gradient Flows of One-Homogeneous Functionals
In: Analysis & Pde (2019)
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Asymptotic profiles of nonlinear homogeneous evolution equations of gradient flow type
In: Journal of Evolution Equations (2019)
Robust Blind Image Fusion for Misaligned Hyperspectral Imaging Data
In: Proceedings in Applied Mathematics and Mechanics 18 (2018), p. 1 - 2
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Blind image fusion for hyperspectral imaging with the directional total variation
In: Inverse Problems 34 (2018)
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Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem
In: Computing and Visualization in Science (2018)
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