| 2026 |
07. September |
14:30 |
SR 127.11, IDea_Lab |
Luca Calatroni (University of Genoa): Learning spatially adaptive regularisation for computational imaging problemsAbstract: Modern computational imaging increasingly calls for methods that combine physical models of image formation with the flexibility of data-driven learning. In this talk, I will present an overview of my research at this interface, focusing on hybrid reconstruction methods that retain the mathematical structure and interpretability of variational models while learning problem-dependent components.
I will take as an example the spatially adaptive Total Variation (TV) and Total Generalised Variation (TGV) regularisation models, in which regularisation strength varies across the image to better preserve edges, smooth regions, and fine details. I will discuss different strategies for estimating these parameter maps, ranging from statistical principles to bilevel optimisation and neural networks embedded within unrolled reconstruction algorithms. Applications to image denoising and accelerated MRI will illustrate how physics-aware learning can produce flexible and interpretable reconstruction methods, even when reference images or large training datasets are unavailable. |
| 2026 |
24. August |
14:30 |
SR 127.11, IDea_Lab |
Philipp Guth & Jesper Schröder (RICAM Linz): Dynamic output-feedback stabilization of uncertain linear dynamics via digital twinsAbstract: Differential equations with uncertain parameters provide a natural framework for modeling incomplete knowledge, measurement errors, and external disturbances. In control applications, such uncertainties can significantly affect system dynamics and pose challenges for the design of reliable feedback laws. This talk presents a computational framework for stabilization and control of uncertain linear dynamical systems, with a particular focus on the transition from offline uncertainty-aware controller design to online, data-driven system reconstruction.
In the first part, we consider ensemble stabilization of linear systems with parametric uncertainty. Feedback laws are constructed using sampling-based approaches and generalized polynomial chaos expansions, yielding controllers that account for variability across the underlying parameter ensemble and provide robust closed-loop performance.
The second part extends this framework toward digital twins by coupling feedback control with sequential Bayesian parameter estimation and observer design. A virtual model evolves alongside the physical system and simultaneously serves as an observer, parameter estimator, and feedback controller. Measurements from the controlled system are used to reconstruct its state and continuously update uncertain model parameters, while the virtual model generates stabilizing feedback. Numerical experiments illustrate the effectiveness of both approaches and demonstrate their potential for reliable closed-loop control in the presence of model uncertainty. |
| 2026 |
19. May |
14:30 |
SR 127.11, IDea_Lab |
Dr. Kostas Papafitsoros (Queen Mary University of London): Combining model-based regularisation with neural network-inferred spatiotemporally varying regularisation parameter maps for inverse imaging problemsAbstract: Combining model-based methods with data-driven approaches, typically based on deep learning, has become increasingly popular for solving inverse imaging problems, ranging from classical tasks such as image denoising to more advanced applications like dynamic Magnetic Resonance Image (MRI) reconstruction. On one hand, model-based methods offer interpretability and reconstruction guarantees. On the other hand, approaches relying on deep learning leverage large datasets as well as the versatility of neural networks to achieve state-of-the-art performance. Their combination seeks to bring together the strengths of both worlds. In this talk, we will present an overview of recent approaches that perform this combination by employing deep neural networks to infer spatially and also temporally adaptive regularisation maps. We will start with a general overview of theoretical properties of weighted versions of classical regularisers like Total Variation (TV) and Total Generalised Variation (TGV) focusing on the regularity of the regularisation parameter maps. We will then describe our main approach which employs a convolutional neural network to estimate these maps, combined with an unrolled algorithmic scheme to solve the image reconstruction problem. For the latter, we consider several model-based approaches including TV, TGV and convolutional synthesis regularisation. We discuss both supervised and self-supervised strategies for training the overall network and we provide numerical results for image denoising and (dynamic) MRI. |
| 2026 |
20. April |
14:30 |
SR 127.11, IDea_Lab |
Dr. Juan Ricardo Muñoz (University of Dubrovnik): Schatten Norm Estimates for Lyapunov Gramians in Operator ScalesAbstract: We analyze the structure of observability Gramians for infinite-dimensional control systems via the Lyapunov equation $AX+XA^* = -BB^*$. Our approach provides explicit eigenvalue decay and Schatten norm estimates that directly relate the Gramian to the spectral properties of the generator and the regularity of the control operator. These abstract results naturally extend existing ones to singular and unbounded controls, and further open the way to generalizations toward anomalous diffusion models. We validate the theory on heat equation benchmarks with both distributed and pointwise actuators, demonstrating how the estimates accurately capture spectral decay and conditioning. |
| 2026 |
19. January |
14:30 |
Open Space, IDea_Lab |
Prof. Leon Bungert (University of Würzburg): 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 |
SR 127.11, IDea_Lab |
Sascha Beutler (University of Münster): 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. |
| 2025 |
20. October |
14:30 |
SR 127.11, IDea_Lab |
Muhamed Kuric (TU Graz): The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse ProblemsAbstract: We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent variable model, which we refer to as a Gaussian latent machine. This leads to a general sampling approach that unifies and generalizes many existing sampling algorithms in the literature. Most notably, it yields a highly efficient and effective two-block Gibbs sampling approach in the general case, while also specializing to direct sampling algorithms in particular cases. Finally, we present detailed numerical experiments that demonstrate the efficiency and effectiveness of our proposed sampling approach across a wide range of prior and posterior sampling problems from Bayesian imaging. |
