| 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. |
