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pro vyhledávání: '"Beinert, Robert"'
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 related to the sliced Wasserstein distance and facilitates classificat
Externí odkaz:
http://arxiv.org/abs/2411.16282
Autor:
Beinert, Robert, Bresch, Jonas
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 denoising problem directly on the hyperbolic space, we exploit the Euclide
Externí odkaz:
http://arxiv.org/abs/2410.16149
We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals $\mathcal F_\nu := \text{MMD}_K^2(\cdot, \nu)$ towards given target measures $\nu$ on the real line, where we focus on the negative distan
Externí odkaz:
http://arxiv.org/abs/2408.07498
Autor:
Beinert, Robert, Bresch, Jonas
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 information, and in color restoration tasks. In this paper, we aim to restore $(
Externí odkaz:
http://arxiv.org/abs/2404.13181
Autor:
Beier, Florian, Beinert, Robert
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. Due to meeting this theoretical underpinning, it is a valuable tool for
Externí odkaz:
http://arxiv.org/abs/2403.08612
Autor:
Hagemann, Paul, Hertrich, Johannes, Altekrüger, Fabian, Beinert, Robert, Chemseddine, Jannis, Steidl, Gabriele
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 lik
Externí odkaz:
http://arxiv.org/abs/2310.03054
Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, a convex relaxation of the otherwise nonconvex Tikhonov-regularization for denoising circle-valued data has been proposed by Con
Externí odkaz:
http://arxiv.org/abs/2307.10980
Publikováno v:
Inverse Problems 39(10), article number 105005, 2023
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-known Radon transform and the cumulative density transform, which anal
Externí odkaz:
http://arxiv.org/abs/2304.09092
Autor:
Beinert, Robert, Rezaei, Saghar
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 is notorious to be severe ill posed such that the recovery of the tru
Externí odkaz:
http://arxiv.org/abs/2301.07696
This paper provides results on Wasserstein gradient flows between measures on the real line. Utilizing the isometric embedding of the Wasserstein space $\mathcal P_2(\mathbb R)$ into the Hilbert space $L_2((0,1))$, Wasserstein gradient flows of funct
Externí odkaz:
http://arxiv.org/abs/2301.04441