Johannes Hertrich


j.hertrich (at) ucl.ac.uk

University College London
Department of Computer Science
United Kingdom

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About me

I am a postdoc in mathematical image processing, inverse problems and machine learning at University College London within the Maths4DL project. Moreover, I acquired a Walter Benjamin Fellowship from the German Research Foundation. Previously, I completed my PhD in 2023 at TU Berlin supervised by Gabriele Steidl for which I received the Dr.-Klaus-Körper Prize 2024 of the Association of Applied Mathematics and Mechanics (GAMM). I obtained my BSc and MSc degrees in Mathematics in 2018 and 2020 from TU Kaiserslautern (renamed in 2023 to RPTU). During my BSc and MSc I was supported by a scholarship of the Felix Klein Center for Mathematics.

My brother Christoph is a postdoc in discrete mathematics at Université libre de Bruxelles.

Publications

  • P. Hagemann, J. Hertrich, M. Casfor, S. Heidenreich and G. Steidl (2024).
    Mixed Noise and Posterior Estimation with Conditional DeepGEM.
    (arXiv Preprint#2402.02964)
    [arxiv], [code]

  • J. Hertrich (2024).
    Fast Kernel Summation in High Dimensions via Slicing and Fourier Transforms.
    (arXiv Preprint#2401.08260)
    [arxiv], [code]

  • P. Hagemann, J. Hertrich, F. Altekrüger, R. Beinert, J. Chemseddine and G. Steidl (2024).
    Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel.
    International Conference on Learning Representations 2024.
    [www], [arxiv], [code]

  • J. Hertrich, C. Wald, F. Altekrüger and P. Hagemann (2024).
    Generative Sliced MMD flows with Riesz kernels.
    International Conference on Learning Representations 2024.
    [www], [arxiv], [code]

  • J. Hertrich, M. Gräf, R. Beinert and G. Steidl (2024).
    Wasserstein Steepest Descent Flows of Discrepancies with Riesz Kernels.
    Journal of Mathematical Analysis and Applications, vol. 531, 127829.
    [doi], [arxiv]

  • M. Piening, F. Altekrüger, J. Hertrich, P. Hagemann, A. Walther and G. Steidl (2023).
    Learning from Small Data Sets: Patch-based Regularizers in Inverse Problems for Image Reconstruction.
    (arXiv Preprint#2312.16611)
    [arxiv], [code]

  • F. Altekrüger, J. Hertrich and G. Steidl (2023).
    Neural Wasserstein Gradient Flows for Maximum Mean Discrepancies with Riesz Kernels.
    International Conference on Machine Learning 2023.
    Proceedings of Machine Learning Research, vol. 202, pp. 664-690.
    [www], [arxiv], [code], [5-min video]

  • F. Altekrüger and J. Hertrich (2023).
    WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution.
    SIAM Journal on Imaging Sciences, vol. 16(3), pp. 1033-1067.
    [doi], [arxiv], [code]

  • F. Altekrüger, A. Denker, P. Hagemann, J. Hertrich, P. Maass and G. Steidl (2023).
    PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization.
    Inverse Problems, vol. 39, no. 6.
    [doi], [arxiv], [code]

  • J. Hertrich, R. Beinert, M. Gräf and G. Steidl (2023).
    Wasserstein Gradient Flows of the Discrepancy with Distance Kernel on the Line.
    L. Calatroni, M. Donatelli, S. Morigi, M. Prato and M. Santacesaria (eds.)
    Scale Space and Variational Methods in Computer Vision.
    Lecture Notes in Computer Science, 14009, 431-443.
    [doi], [arxiv]

  • J. Hertrich (2023).
    Proximal Residual Flows for Bayesian Inverse Problems.
    L. Calatroni, M. Donatelli, S. Morigi, M. Prato and M. Santacesaria (eds.)
    Scale Space and Variational Methods in Computer Vision.
    Lecture Notes in Computer Science, 14009, 210-222.
    [doi], [arxiv], [code]

  • G.S. Alberti, J. Hertrich, M. Santacesaria and S. Sciutto (2023).
    Manifold Learning by Mixture Models of VAEs for Inverse Problems.
    (arXiv Preprint#2303.15244)
    [arxiv], [code]

  • P. Hagemann, J. Hertrich and G. Steidl (2023).
    Generalized Normalizing Flows via Markov Chains.
    Elements in Non-local Data Interactions: Foundations and Applications.
    Cambridge University Press.
    [doi], [arxiv], [code]

  • D.P.L. Nguyen, J. Hertrich, J.-F. Aujol and Y. Berthoumieu (2023).
    Image super-resolution with PCA reduced generalized Gaussian mixture models in materials science.
    Inverse Problems and Imaging, vol. 17, pp. 1165-1192.
    [doi], [hal]

  • P. Hagemann, J. Hertrich and G. Steidl (2022).
    Stochastic Normalizing Flows: a Markov Chains Viewpoint.
    SIAM/ASA Journal on Uncertainty Quantification, vol. 10, pp. 1162-1190.
    [doi], [arxiv], [code]

  • J. Hertrich, A. Houdard and C. Redenbach (2022).
    Wasserstein Patch Prior for Image Superresolution.
    IEEE Transactions on Computational Imaging, vol. 8, pp. 693-704.
    [doi], [arxiv], [code]

  • J. Hertrich and G. Steidl (2022).
    Inertial Stochastic PALM and Applications in Machine Learning.
    Sampling Theory, Signal Processing, and Data Analysis, vol. 20, no. 4.
    [doi], [arxiv], [code]

  • J. Hertrich, D.P.L. Nguyen, J.-F. Aujol, D. Bernard, Y. Berthoumieu, A. Saadaldin and G. Steidl (2022).
    PCA reduced Gaussian mixture models with application in superresolution.
    Inverse Problems and Imaging, vol. 16, pp. 341-366.
    [doi], [arxiv], [code]

  • J. Hertrich, F. Ba and G. Steidl (2022).
    Sparse Mixture Models Inspired by ANOVA Decompositions.
    Electronic Transactions on Numerical Analysis, vol. 55, pp. 142-168.
    [doi], [arxiv], [code]

  • J. Hertrich, S. Neumayer and G. Steidl (2021).
    Convolutional Proximal Neural Networks and Plug-and-Play Algorithms.
    Linear Algebra and its Applications, vol 631, pp. 203-234.
    [doi], [arxiv], [code]

  • M. Hasannasab, J. Hertrich, F. Laus and G. Steidl (2021).
    Alternatives to the EM Algorithm for ML-Estimation of Location, Scatter Matrix and Degree of Freedom of the Student-t Distribution.
    Numerical Algorithms, vol. 87, pp. 77-118.
    [doi], [arxiv], [code]

  • T. Batard, J. Hertrich and G. Steidl (2020).
    Variational models for color image correction inspired by visual perception and neuroscience.
    Journal of Mathematical Imaging and Vision, vol. 62, pp. 1173-1194.
    [doi], [hal]

  • M. Hasannasab, J. Hertrich, S.Neumayer, G. Plonka, S. Setzer and G. Steidl (2020).
    Parseval Proximal Neural Networks.
    Journal of Fourier Analysis and Applications, vol. 26, no. 59.
    [doi], [arxiv], [code]

  • J. Hertrich, M. Bačák, S. Neumayer, G. Steidl (2020).
    Minimal Lipschitz and ∞-Harmonic Extensions of Vector-Valued Functions on Finite Graphs.
    Information and Inference: A Journal of the IMA, vol. 9, pp. 935–959.
    [doi], [arxiv], [code]

  • J. Hertrich, M. Bačák, S. Neumayer, G. Steidl (2019).
    Minimal Lipschitz extensions for vector-valued functions on finite graphs.
    M. Burger, J. Lellmann and J. Modersitzki (eds.)
    Scale Space and Variational Methods in Computer Vision.
    Lecture Notes in Computer Science, 11603, 183-195.
    [doi], [code]

Theses

  • Proximal Neural Networks and Stochastic Normalizing Flows for Inverse Problems.
    PhD Thesis, 2023.
    TU Berlin
    [doi]

  • Superresolution via Student-t Mixture Models.
    Master Thesis, 2020.
    TU Kaiserslautern

  • Infinity Laplacians on Scalar- and Vector-valued Functions and Optimal Lipschitz Extensions on Graphs.
    Bachelor Thesis, 2018.
    TU Kaiserslautern
Plain Academic