95 citations · 768 across the 58 of their papers we have counts for
66 papers
A Study of Particle Motion in the Presence of Clusters
Christian Wald, Gabriele Steidl
The motivation for this study came from the task of analysing the kinetic behavior of single molecules in a living cell based on Single Molecule Localization Microscopy. Given meas…
Denoising of Sphere- and SO(3)-Valued Data by Relaxed Tikhonov Regularization
Robert Beinert, Jonas Bresch, Gabriele Steidl
Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, a convex relaxation of the otherwise nonconvex Tikhonov-re…
Generalized Iterative Scaling for Regularized Optimal Transport with Affine Constraints: Application Examples
Johannes von Lindheim, Gabriele Steidl
We demonstrate the relevance of an algorithm called generalized iterative scaling (GIS) or simultaneous multiplicative algebraic reconstruction technique (SMART) and its rescaled b…
Sliced Optimal Transport on the Sphere
Michael Quellmalz, Robert Beinert, Gabriele Steidl
Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-…
Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems
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 measu…
Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation
Paul Hagemann, Sophie Mildenberger, Lars Ruthotto +2
Score-based diffusion models (SBDM) have recently emerged as state-of-the-art approaches for image generation. Existing SBDMs are typically formulated in a finite-dimensional setti…
Wasserstein Gradient Flows of the Discrepancy with Distance Kernel on the Line
Johannes Hertrich, Robert Beinert, Manuel Gräf +1
This paper provides results on Wasserstein gradient flows between measures on the real line. Utilizing the isometric embedding of the Wasserstein space in…
Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernels
Fabian Altekrüger, Johannes Hertrich, Gabriele Steidl
Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous o…
Wasserstein Steepest Descent Flows of Discrepancies with Riesz Kernels
Johannes Hertrich, Manuel Gräf, Robert Beinert +1
The aim of this paper is twofold. Based on the geometric Wasserstein tangent space, we first introduce Wasserstein steepest descent flows. These are locally absolutely continuous c…
Motion Detection in Diffraction Tomography by Common Circle Methods
Michael Quellmalz, Peter Elbau, Otmar Scherzer +1
The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an o…
On Assignment Problems Related to Gromov-Wasserstein Distances on the Real Line
Robert Beinert, Cosmas Heiss, Gabriele Steidl
Let and , , be real numbers. We show by an example that the assignment problem $$ \max_{σ\in S_n} F_σ(x,y) := \frac12 \sum_{…
PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization
Fabian Altekrüger, Alexander Denker, Paul Hagemann +3
Learning neural networks using only few available information is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a power…
Multi-Marginal Gromov-Wasserstein Transport and Barycenters
Florian Beier, Robert Beinert, Gabriele Steidl
Gromov-Wasserstein (GW) distances are combinations of Gromov-Hausdorff and Wasserstein distances that allow the comparison of two different metric measure spaces (mm-spaces). Due t…
Lagrangian Motion Magnification with Double Sparse Optical Flow Decomposition
Philipp Flotho, Cosmas Heiss, Gabriele Steidl +1
Microexpressions are fast and spatially small facial expressions that are difficult to detect. Therefore motion magnification techniques, which aim at amplifying and hence revealin…
Quasi -Firmly Nonexpansive Mappings in Wasserstein Spaces
Arian Bërdëllima, Gabriele Steidl
This paper introduces the concept of quasi -firmly nonexpansive mappings in Wasserstein spaces over and analyzes properties of these mappings. We prove that for qu…
On a linear Gromov-Wasserstein distance
Florian Beier, Robert Beinert, Gabriele Steidl
Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal tr…
Generalized Normalizing Flows via Markov Chains
Paul Hagemann, Johannes Hertrich, Gabriele Steidl
Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via…
Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint
Paul Hagemann, Johannes Hertrich, Gabriele Steidl
To overcome topological constraints and improve the expressiveness of normalizing flow architectures, Wu, Köhler and Noé introduced stochastic normalizing flows which combine deter…
On the Dynamical System of Principal Curves in
Robert Beinert, Arian Bërdëllima, Manuel Gräf +1
Principal curves are natural generalizations of principal lines arising as first principal components in the Principal Component Analysis. They can be characterized from a stochast…
An Image Registration Model in Electron Backscatter Diffraction
Manuel Gräf, Sebastian Neumayer, Ralf Hielscher +3
Recently, variational methods were successfully applied for computing the optical flow in gray and RGB-valued image sequences. A crucial assumption in these models is that pixel-va…
Sparse Mixture Models inspired by ANOVA Decompositions
Johannes Hertrich, Fatima Antarou Ba, Gabriele Steidl
Inspired by the analysis of variance (ANOVA) decomposition of functions we propose a Gaussian-Uniform mixture model on the high-dimensional torus which relies on the assumption tha…
Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations
Clemens Kirisits, Michael Quellmalz, Monika Ritsch-Marte +3
In this paper, we study the mathematical imaging problem of optical diffraction tomography (ODT) for the scenario of a microscopic rigid particle rotating in a trap created, for in…
On -Firmly Nonexpansive Operators in -Uniformly Convex Spaces
Arian Bërdëllima, Gabriele Steidl
We introduce the class of -firmly nonexpansive and quasi -firmly nonexpansive operators on -uniformly convex Banach spaces. This extends the existing notion from Hilbert s…
On approximate operator representations of sequences in Banach spaces
Ole Christensen, Marzieh Hasannasab, Gabriele Steidl
Generalizing results by Halperin et al., Grivaux recently showed that any linearly independent sequence in a separable Banach space can be represented as…