Research Unit DESY
At the beginning of the imaging pipeline is the data acquisition, which measures the change of an emitted signal when interacting with sample.
Inverse Problems: we focus on problems at the beginning of the imaging pipeline related to data acquisition and image formation. This is a crucial step in the pipeline, since information lost or not measured at this stage can hardly be recovered in later stages.
In the data acquisition, the change of some emitted signal interacting with the sample is measured. In order to produce meaningful images, an image reconstruction step is necessary. To achieve this task a mathematical model of the forward process leading to data generation has to be developed and then inverted to compute the image of interest. This process is called an inverse problem, whose stable solution relies on further a-priori knowledge or even training data about the type of images to be reconstructed. The development of algorithms for image reconstruction with highest quality is a major research topic for us.
The quality of the reconstructions is controlled via uncertainty quantification methods and feedback to the data acquisition is given by optimal experimental design techniques. Further important research questions investigated concern the compression of large scale data as well as problems at the edge to further steps in the pipeline such as denoising and registration.
Publications
4725570
HI Science Unit DESY
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https://helmholtz-imaging.de/apa-bold-title.csl
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creator
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https://helmholtz-imaging.de/wp-content/plugins/zotpress/
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Burger, M., Humpert, I., & Pietschmann, J.-F. (2023). Dynamic Optimal Transport on Networks. ESAIM: Control, Optimisation and Calculus of Variations, 29, 54. https://doi.org/10.1051/cocv/2023027
Burger, M., Schuster, T., & Wald, A. (2023). Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces (arXiv:2310.08600). arXiv. http://arxiv.org/abs/2310.08600
Burger, M., Jansen, S., Hölzer, K., Kaden, T., Kuger, L., Lösch, H., Petrak, S., Rieger, T., & Schönmuth, T. (n.d.). Multiple scatter correction for single plane Compton camera imaging in nuclear decommissioning. PAMM, n/a(n/a), e202300281. https://doi.org/10.1002/pamm.202300281
Burger, M., Kabri, S., Korolev, Y., Roith, T., & Weigand, L. (2025). Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization. arXiv Preprint arXiv:2501.03096.
Burger, M., Loy, N., & Rossi, A. (2025). Asymptotic and Stability Analysis of Kinetic Models for Opinion Formation on Networks: An Allen�Cahn Approach. SIAM Journal on Applied Dynamical Systems.
Burger, M., Erbar, M., Hoffmann, F., Matthes, D., & Schlichting, A. (2025). Covariance-modulated optimal transport and gradient flows. Archive for Rational Mechanics and Analysis.
Deidda, P., Burger, M., Putti, M., & Tudisco, F. (2024). The graph $\infty$-Laplacian eigenvalue problem (arXiv:2410.19666). arXiv. https://doi.org/10.48550/arXiv.2410.19666
Ehrhardt, M. J., Kuger, L., & Schönlieb, C.-B. (2024). Proximal Langevin Sampling With Inexact Proximal Mapping. SIAM Journal on Imaging Sciences, 17(3), 1729–1760. https://doi.org/10.1137/23M1593565
Fazeny, A., Tenbrinck, D., & Burger, M. (2023). Hypergraph p-Laplacians, Scale Spaces, and Information Flow in Networks. In L. Calatroni, M. Donatelli, S. Morigi, M. Prato, & M. Santacesaria (Eds.), Scale Space and Variational Methods in Computer Vision (pp. 677–690). Springer International Publishing. https://doi.org/10.1007/978-3-031-31975-4_52
Fazeny, A., Tenbrinck, D., Lukin, K., & Burger, M. (2024). Hypergraph p-Laplacians and Scale Spaces. Journal of Mathematical Imaging and Vision, 66(4), 529–549. https://doi.org/10.1007/s10851-024-01183-0
Fazeny, A., Burger, M., & Pietschmann, J.-F. (2024). Optimal transport on gas networks (arXiv:2405.01698). arXiv. https://doi.org/10.48550/arXiv.2405.01698
Fazeny, A., Burger, M., & Pietschmann, J.-F. (2025). Optimal transport on gas networks. European Journal of Applied Mathematics.
Kabri, S., Roith, T., Tenbrinck, D., & Burger, M. (2023). Resolution-Invariant Image Classification Based on Fourier Neural Operators. In L. Calatroni, M. Donatelli, S. Morigi, M. Prato, & M. Santacesaria (Eds.), Scale Space and Variational Methods in Computer Vision (pp. 236–249). Springer International Publishing. https://doi.org/10.1007/978-3-031-31975-4_18
Kabri, S., Auras, A., Riccio, D., Bauermeister, H., Benning, M., Moeller, M., & Burger, M. (2022). Convergent Data-driven Regularizations for CT Reconstruction (arXiv:2212.07786). arXiv. https://doi.org/10.48550/arXiv.2212.07786
Kabri, S., Auras, A., Riccio, D., Bauermeister, H., Benning, M., Moeller, M., & Burger, M. (2024). Convergent Data-Driven Regularizations for CT Reconstruction. Communications on Applied Mathematics and Computation, 6(2), 1342–1368. https://doi.org/10.1007/s42967-023-00333-2
Ran, Y., Guo, Z., Li, J., Li, Y., Burger, M., & Wu, B. (2024). A Tunable Despeckling Neural Network Stabilized via Diffusion Equation (arXiv:2411.15921). arXiv. https://doi.org/10.48550/arXiv.2411.15921
Roith, T. (2024). Consistency, Robustness and Sparsity for Learning Algorithms. https://open.fau.de/handle/openfau/30802
Shi, K., & Burger, M. (2024). Hypergraph $p$-Laplacian equations for data interpolation and semi-supervised learning (arXiv:2411.12601). arXiv. https://doi.org/10.48550/arXiv.2411.12601
Shi, K., & Burger, M. (2024). Hypergraph $p$-Laplacian regularization on point clouds for data interpolation (arXiv:2405.01109). arXiv. https://doi.org/10.48550/arXiv.2405.01109
Shi, K., & Burger, M. (2024). Continuum limit of $p$-biharmonic equations on graphs (arXiv:2404.19689). arXiv. https://doi.org/10.48550/arXiv.2404.19689
Shi, K., & Burger, M. (2025). Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning. Journal of Scientific Computing.
Shi, K., & Burger, M. (2025). Hypergraph p-laplacian regularization on point clouds for data interpolation. Nonlinear Analysis.
Weigand, L., Roith, T., & Burger, M. (2024). Adversarial flows: A gradient flow characterization of adversarial attacks (arXiv:2406.05376). arXiv. https://doi.org/10.48550/arXiv.2406.05376
Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics - Nöldner - 2023 - ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik - Wiley Online Library. (n.d.). Retrieved January 29, 2024, from https://onlinelibrary.wiley.com/doi/10.1002/zamm.202300101
Learning in Image Reconstruction: A Cautionary Tale | SIAM. (2024, October 1). Society for Industrial and Applied Mathematics. https://www.siam.org/publications/siam-news/articles/learning-in-image-reconstruction-a-cautionary-tale/
Inverse Problems on Large Scales: Mathematical Modelling and Computational Methods. (2024). De Gruyter. https://doi.org/10.1515/9783111357270
Other Researches
Projects
Helmholtz Imaging Projects are granted to cross-disciplinary research teams that identify innovative research topics at the intersection of imaging and information & data science, initiate cross-cutting research collaborations, and thus underpin the growth of the Helmholtz Imaging network. These annual calls are based on the general concept for Helmholtz Imaging and are in line with the future topics of the Initiative and Networking Fund (INF).
Research Unit MDC
The Research Unit at MDC focuses on integrating heterogeneous imaging data across modalities, scales, and time. We develop concepts and algorithms for generic processing, stitching, fusion, and visualization of large, high-dimensional datasets.
Our aim is to enable seamless analysis of complex imaging data without restrictions on the underlying modalities.
Research Unit DKFZ
The Research Unit at DKFZ focuses on the downstream stages of the imaging pipeline, developing robust methods for automated image analysis and emphasizing rigorous validation.
Our goal is to enable trustworthy and generalizable AI across scientific imaging domains.
Publications
Helmholtz Imaging captures the world of science. Discover unique data sets, ready-to-use software tools, and top-level research papers. The platform’s output originates from our research groups as well as from projects funded by us, theses supervised by us and collaborations initiated through us. Altogether, this showcases the whole diversity of Helmholtz Imaging.