| 2026 |
19. January |
14:30 |
Open Space, IDea_Lab |
Prof. Leon Bungert: Robustness on the interface of geometry and probabilityAbstract: In this talk I will present the latest developments in the analysis of adversarial machine learning. For this I will build on the geometric interpretation of adversarial training as regularization problem for a nonlocal perimeter of the decision boundary. This perspective allows one to use tools from calculus of variations to derive the asymptotics of adversarial training for small adversarial budgets as well as to rigorously connect it to a mean curvature flow of the decision boundary. We also show that adversarial training is embedded in a larger family of probabilistically robust problems. This is joint work with N. García Trillos, R. Murray, K. Stinson, and T. Laux, and others. |
| 2025 |
17. November |
14:30 |
at SR 127.11, IDea_Lab |
Sascha Beutler: From Motion Estimation to Active Correction in Intravital Fluorescence MicroscopyAbstract: Physiological motion from respiration and cardiac cycles poses significant challenges for fluorescence microscopy of living tissues. Since even small motions can move the cell out of the focal plane, it is particularly difficult to observe the same single cell over time. In this talk, I will first describe the nature of data produced by fluorescence microscopes, discuss key considerations for in vivo measurements, and explain which system parameters we can control to actively correct for motion during and in between image acquisition. I will then present a motion correction approach that leverages the periodicity of physiological motion, specifically under the assumption that a cylindrical structure, such as a blood vessel, is being observed. Finally, I will provide an overview of our research involving shape spaces, outlining how this infinite-dimensional geometric framework relates to the motion problem in microscopy and how we aim to integrate these methods to improve motion correction in the future. |
| 2025 |
14. November |
15:00 |
at Stremayrgasse 16, BMT 03 094, TU Graz |
Richard Huber: The L2-Optimal Discretization of Tomographic Projection OperatorsAbstract: Tomographic inverse problems remain a cornerstone of medical investigations, allowing the visualization of patients' interior features. While the infinite-dimensional operators modeling the measurement process (e.g., the Radon transform) are well understood, in practice, one can only observe finitely many measurements and employ finitely many computations in reconstruction. Thus, proper discretization of these operators is crucial. Different discretization approaches show distinct strengths regarding the approximation quality of the forward- or backward projections. Hence, it is common to employ distinct discretization frameworks for the two said operators, creating a non-adjoint pair of operators. Using such unmatched projection pairs in iterative methods can be problematic, as theoretical convergence guarantees of many iterative methods are based on matched operators. We present a novel theoretical framework for designing an $L^2$-optimal discretization of the forward projection. Curiously, the adjoint of said optimal discretization is the optimal discretization for the backprojection, yielding a matched discretization framework for which both the forward and backward discretization (being the optimal choices) converge, thus eliminating the need for unmatched operator pairs. In the parallel beam case, this optimal discretization is the well-known strip model for discretization, while in the fanbeam case, a novel weighted strip model is optimal. |
