26 citations · 156 across the 36 of their papers we have counts for
39 papers
A Discrete Radon Transform Based on the Area of Cube-Plane Intersection
Robert Beinert, Jonas Bresch, Michael Quellmalz
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an a…
Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition
Matthias Beckmann, Robert Beinert, Jonas Bresch
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely…
Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport
Moritz Piening, Robert Beinert
Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wass…
A Novel Sliced Fused Gromov-Wasserstein Distance
Moritz Piening, Robert Beinert
The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both dista…
Denoising Multi-Color QR Codes and Stiefel-Valued Data by Relaxed Regularizations
Robert Beinert, Jonas Bresch
The handling of manifold-valued data, for instance, plays a central role in color restoration tasks relying on circle- or sphere-valued color models, in the study of rotational or…
Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification
Matthias Beckmann, Robert Beinert, Jonas Bresch
The Radon cumulative distribution transform (R-CDT), is an easy-to-compute feature extractor that facilitates image classification tasks especially in the small data regime. It is…
Slicing the Gaussian Mixture Wasserstein Distance
Moritz Piening, Robert Beinert
Gaussian mixture models (GMMs) are widely used in machine learning for tasks such as clustering, classification, image reconstruction, and generative modeling. A key challenge in w…
Joint Metric Space Embedding by Unbalanced OT with Gromov-Wasserstein Marginal Penalization
Florian Beier, Moritz Piening, Robert Beinert +1
We propose a new approach for unsupervised alignment of heterogeneous datasets, which maps data from two different domains without any known correspondences to a common metric spac…
Max-Normalized Radon Cumulative Distribution Transform for Limited Data Classification
Matthias Beckmann, Robert Beinert, Jonas Bresch
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely…
Denoising Hyperbolic-Valued Data by Relaxed Regularizations
Robert Beinert, Jonas Bresch
We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the deno…
Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions
Richard Duong, Viktor Stein, Robert Beinert +2
We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals towards given target measu…
Denoising Sphere-Valued Data by Relaxed Total Variation Regularization
Robert Beinert, Jonas Bresch
Circle- and sphere-valued data play a significant role in inverse problems like magnetic resonance phase imaging and radar interferometry, in the analysis of directional informatio…
Tangential Fixpoint Iterations for Gromov-Wasserstein Barycenters
Florian Beier, Robert Beinert
The Gromov-Wasserstein (GW) transport problem is a relaxation of classic optimal transport, which seeks a transport between two measures while preserving their internal geometry. D…
Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel
Paul Hagemann, Johannes Hertrich, Fabian Altekrüger +3
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…
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…
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-…
Prony-Based Super-Resolution Phase Retrieval of Sparse, Multivariate Signals
Robert Beinert, Saghar Rezaei
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem…
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…
Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography with an Arbitrarily Moving Object
Robert Beinert, Michael Quellmalz
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus li…
Multi-marginal Approximation of the Linear Gromov-Wasserstein Distance
Florian Beier, Robert Beinert
Recently, two concepts from optimal transport theory have successfully been brought to the Gromov--Wasserstein (GW) setting. This introduces a linear version of the GW distance and…
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…
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_{…
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…
Total variation-based reconstruction and phase retrieval for diffraction tomography
Robert Beinert, Michael Quellmalz
In optical diffraction tomography (ODT), the three-dimensional scattering potential of a microscopic object rotating around its center is recovered by a series of illuminations wit…