IFML Seminar: 08/28/26 - Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using Preconditioned Langevin Sampling

Abstract: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high-quality MRI reconstructions with uncertainty quantification from highly undersampled k-space data. However, sampling methods such as diffusion posterior sampling (DPS) and likelihood annealing suffer from long reconstruction times and the need for parameter tuning. Crucially, these parameters often need to be tuned for different measurement models, limiting some of the practical flexibility offered by the Bayesian approach.

We observed that the practical difficulties encountered when sampling from the posterior distribution arise from the ill-conditioning of the problem. In practice, this requires small step sizes and many noise scales, which can make sampling prohibitively slow. We tackle this problem by preconditioning the sampling process.

In this talk, we will recap the fundamentals of MR image reconstruction and score-based diffusion modeling with annealed ULA sampling to motivate the proposed preconditioned sampling strategy. We will then show that the proposed approach substantially improves sampling efficiency while providing reliable posterior sampling across Cartesian and non-Cartesian accelerated MRI, without requiring measurement-model- specific parameter retuning.

This talk is based on joint work with Tina Holliber, Jon Tamir, and Martin Uecker.
 

Bio: Moritz Blumenthal is a postdoctoral researcher at Graz University of Technology and Boston Children’s Hospital. His research interests include computational MRI, with a focus on deep-learning-based reconstruction, Bayesian reconstruction with diffusion priors, physics-based reconstruction, and memory-efficient implementations of computational algorithms. He received his PhD in mathematical sciences from the University of Göttingen in 2024 under the supervision of Prof. Martin Uecker.

Zoom Link: https://utexas.zoom.us/j/85330568382