Research
Inverse problems in medical science aim to reconstruct physiological parameters or internal body structures from indirect measurements. Examples include optical imaging, where tissue activity is inferred from light scattering, and radiation therapy planning, where beam parameters are optimised to achieve a desired three-dimensional dose distribution.
These problems are typically high-dimensional, ill-posed, and non-convex. At the same time, the underlying parameters often exhibit intrinsic geometric structure that can be naturally modelled using manifolds.
Our research develops Riemannian optimisation methods that exploit this structure, combined with multilevel techniques arising from discretisations on multiple grids. This approach improves scalability and computational efficiency.
A key challenge is to effectively address the non-convex nature of these problems while maintaining robustness. By integrating geometric and multilevel ideas, we aim to provide efficient optimisation tools for medical imaging and therapy.
Publications
- Multilevel Optimization: Geometric Coarse Models and Convergence Analysis, International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2025. [DOI] [arXiv]
- Information Geometry of Exponentiated Gradient: Convergence beyond L-Smoothness, International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2025. [DOI] [arXiv]
Mathematikon, Office 4/229
