Mathematical Methods in MRI - SFB MR-DYNAMO Workshop

Session

Contributed Talks: Session 5

21 May 2026, 11:20

HS BMT (BMTEG138), Stremayrgasse 16

Conveners

Contributed Talks: Session 5

• Christian Clason (University of Graz)

38. An inertial Langevin algorithm

Mr Alexander Falk (TU Graz)

21/05/2026, 11:20

We present a novel method for drawing samples from Gibbs distributions with densities of the form π(x)∝exp(−U(x)). The method accelerates the unadjusted Langevin algorithm by introducing an inertia term similar to Polyak's heavy ball method, together with a corresponding noise rescaling. Interpreting the scheme as a discretization of kinetic Langevin dynamics, we prove ergodicity (in...

34. Preconditioned Langevin sampling for Bayesian imaging

Dr Andreas Habring

21/05/2026, 11:45

In this talk we consider time- and space-dependent preconditioning for Langevin sampling from posteriors arising in Bayesian inverse imaging problems, in particular, MRI. Inspired by quasi-Newton methods in optimization, we consider learned preconditioners which use curvature information to accelerate sampling. We provide a careful theoretical analysis of the sampling methods based on the...

16. Fast and robust diffusion posterior sampling for MR image reconstruction using the preconditioned unadjusted Langevin algorithm

Ms Tina Holliber (Graz University of Technology, Institute of Biomedical Imaging)

21/05/2026, 12:10

Introduction Diffusion models employed as prior knowledge have demonstrated strong performance in MRI reconstruction. A principal advantage of this probabilistic framework is that the variability across generated samples enables uncertainty quantification. Incorporating the likelihood term directly into the diffusion process, however, yields intractable expressions that are typically...