52 citations · 270 across the 25 of their papers we have counts for
6 papers · 1 filter
Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction
Moritz Piening, Fabian Altekrüger, Johannes Hertrich +3
The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by u…
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…
Generative Sliced MMD Flows with Riesz Kernels
Johannes Hertrich, Christian Wald, Fabian Altekrüger +1
Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels $K(x,y) = - \|x-y\|^…
Manifold Learning by Mixture Models of VAEs for Inverse Problems
Giovanni S. Alberti, Johannes Hertrich, Matteo Santacesaria +1
Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifo…
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…