Inverse Problems Meeting 29-30 October 2026

Masterclass on numerical linear algebra for inverse problems

10.00 - 10.30 Coffee/tea

10.30 - 11.30 Masterclass part I - Krylov subspace methods for regularization in inverse problems by Maike Meier (RUG)

Krylov subspace methods have long been used in inverse problems for iterative or Tikhonov regularization. Recently, there has been renewed attention for the applicability of these algorithms for more computationally challenging types of regularization as total variation. The linear algebraic interpretation of Krylov methods offer one big upside compared to standard optimization tools: the automatic determination of a regularization parameter via hybrid Krylov subspace methods. This talk will introduce these algorithms and demonstrate their performance on large-scale, 3D image reconstruction problems. Finally, we will shortly touch on the Bayesian interpretation and the use of Krylov methods for uncertainty quantification.

11:30 - 12:30 Masterclass part II - Numerical linear algebra in data assimilation by Jemima Tabeart (TU/e)

Data assimilation methods are a particular class of inverse problem where prior information from a dynamical system is combined with observation information to obtain an improved estimate of the state at a given time. I will introduce the variational data assimilation problem, which gives rise to a nonlinear least squares problem. We will investigate how techniques from numerical linear algebra (different solvers, parallelisation, preconditioners) can be used to `solve’ a high-dimensional ill-conditioned problem in a very short wallclock time.

12.30 - 14.00 Lunch break

14.00 - 16.00 Lab tour

16:00 - 18.00 Poster session and drinks

18:30 - 20:00 Dinner at CWI 

09.30 - 10.30 Key note by Martin Benning (UCL London) - Mind the Gap: Bilevel Optimisation with Fenchel-Young Functions

Inverse problems are increasingly solved by combining physics-based variational models with data-driven parameter learning, but standard bilevel optimisation remains computationally demanding because each gradient step typically requires differentiating through an inner optimisation problem. This talk presents a Fenchel-Young perspective that replaces the classical bilevel loss with a gap-function objective, interpretable as a generalised duality gap and, under suitable conditions, as a Bregman distance. The resulting formulation preserves the core modelling structure of variational regularisation while yielding substantially simpler gradients, avoiding repeated solutions of adjoint and fixed-point equations. We will outline key theoretical links to constrained formulations (including Morozov- and Ivanov-type regularisation), discuss variational error estimates with convergence guarantees, and show how the framework extends from scalar to spatially varying regularisation parameters and infimal convolution regularisations. Numerical evidence in compressed sensing and imaging settings indicates comparable reconstruction quality to bilevel baselines at markedly lower computational cost. This is joint work with Alexandra Valavanis (Queen Mary University of London) and Clarice Poon (University of Warwick).

10.30 - 11.00 Coffee break

11:00 – 12:30 Invited talks I

• David Nolte (RUG) - Parameter estimation in coupled fluid-solid systems with application to cardiac biomechanics
• Svetlana Dubinkina (VU) - TBA
• Carlas Sierd Smith (TU Delft) - Super-resolution microscopy

12.30 - 13.30 Lunch break

13:30 – 14:30 Invited talks II

• Emily Anne Frame (CWI) - Neutron imaging for cultural heritage
• Mark Peletier (TU/e) - TBA

14:30 - 15.00 Coffee break

15:00 – 16:00 Invited talks III

• Daan Pelt (Leiden U.) - Deep Learning for Cryo-EM imaging
• TBA

16:00 – 17:00 Closing and drinks