Fabian Altekrüger

Fabian Altekrüger, Paul Hagemann, Gabriele Steidl

Conditional generative models became a very powerful tool to sample from Bayesian inverse problem posteriors. It is well-known in classical Bayesian literature that posterior measures are quite robust with respect to perturbations of both the prior measure and the negative log-likelihood, which includes perturbations of the observations. However, to the best of our knowledge, the robustness of conditional generative models with respect to perturbations of the observations has not been investigated yet. In this paper, we prove for the first time that appropriately learned conditional generative models provide robust results for single observations.

Paul Hagemann, Johannes Hertrich, Fabian Altekrüger et al.

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

Moritz Piening, Fabian Altekrüger, Gabriele Steidl et al.

Contrast enhancement by Gadolinium-based contrast agents (GBCAs) is a vital tool for tumor diagnosis in neuroradiology. Based on brain MRI scans of glioblastoma before and after Gadolinium administration, we address enhancement prediction by neural networks with two new contributions. Firstly, we study the potential of generative models, more precisely conditional diffusion and flow matching, for uncertainty quantification in virtual enhancement. Secondly, we examine the performance of T1 scans from quantitive MRI versus T1-weighted scans. In contrast to T1-weighted scans, these scans have the advantage of a physically meaningful and thereby comparable voxel range. To compare network prediction performance of these two modalities with incompatible gray-value scales, we propose to evaluate segmentations of contrast-enhanced regions of interest using Dice and Jaccard scores. Across models, we observe better segmentations with T1 scans than with T1-weighted scans.