52 citations · 270 across the 25 of their papers we have counts for
26 papers
Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme
Chenguang Duan, Johannes Hertrich, Gabriele Steidl
We propose a neural algorithm for sampling from distributions specified by unnormalized Boltzmann densities. Our approach is based on the Jordan--Kinderlehrer--Otto scheme for the…
Tessellations of Semi-Discrete Flow Matching
Emile Pierret, Johannes Hertrich, Samuel Hurault +1
We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported on finitely many points. This semi-discrete regime is th…
DeepInverse: A Python package for solving imaging inverse problems with deep learning
Julián Tachella, Matthieu Terris, Samuel Hurault +24
DeepInverse is an open-source PyTorch-based library for solving imaging inverse problems. The library covers all crucial steps in image reconstruction from the efficient implementa…
Generative Feature Training of Thin 2-Layer Networks
Johannes Hertrich, Sebastian Neumayer
We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-conv…
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…
Mixed Noise and Posterior Estimation with Conditional DeepGEM
Paul Hagemann, Johannes Hertrich, Maren Casfor +2
Motivated by indirect measurements and applications from nanometrology with a mixed noise model, we develop a novel algorithm for jointly estimating the posterior and the noise par…
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…
Proximal Residual Flows for Bayesian Inverse Problems
Johannes Hertrich
Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal r…
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…
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…
WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution
Fabian Altekrüger, Johannes Hertrich
Exploiting image patches instead of whole images have proved to be a powerful approach to tackle various problems in image processing. Recently, Wasserstein patch priors (WPP), whi…
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…
Wasserstein Patch Prior for Image Superresolution
Johannes Hertrich, Antoine Houdard, Claudia Redenbach
In this paper, we introduce a Wasserstein patch prior for superresolution of two- and three-dimensional images. Here, we assume that we have given (additionally to the low resoluti…
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…
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…
Convolutional Proximal Neural Networks and Plug-and-Play Algorithms
Johannes Hertrich, Sebastian Neumayer, Gabriele Steidl
In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters of full length, we propose a stochastic gradie…
PCA Reduced Gaussian Mixture Models with Applications in Superresolution
Johannes Hertrich, Dang Phoung Lan Nguyen, Jean-Fancois Aujol +4
Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contrib…
Inertial Stochastic PALM (iSPALM) and Applications in Machine Learning
Johannes Hertrich, Gabriele Steidl
Inertial algorithms for minimizing nonsmooth and nonconvex functions as the inertial proximal alternating linearized minimization algorithm (iPALM) have demonstrated their superior…
Parseval Proximal Neural Networks
Marzieh Hasannasab, Johannes Hertrich, Sebastian Neumayer +3
The aim of this paper is twofold. First, we show that a certain concatenation of a proximity operator with an affine operator is again a proximity operator on a suitable Hilbert sp…