Software

Adaptive Finite Difference Method for Total Variation Minimization

  • A Python-package for an adaptive finite difference method for total variation minimization can be found here.
    This code is based on the papers:
    • T. Jacumin and A. Langer, An adaptive finite difference method for total variation minimization, Numerical Algorithms (2025) [link]

DeepTV

  • A Python-package for a neural network approach for total variation minimization can be found here.
    This code is based on the paper:
    • A. Langer and S. Behnamian, DeepTV: A neural network approach for total variation minimization, arXiv preprint arXiv:2409.05569, 2024. [link]

Domain Decomposition for Total Variation Minimization

  • A Julia-package for overlapping domain decomposition methods for a dual total variation problem can be found here.
    This code is based on the paper:
    • S. Hilb and A. Langer, A general decomposition method for a convex problem related to total variation minimization, arXiv preprint arXiv:2211.00101, 2022. [pdf][link]
  • A Matlab-package for overlapping domain decomposition methods for total variation minimization can be found here .

Finite Element Methods for Total Variation Minimization

  • A Julia-package for a finite element method for scalar and vectorial total variation minimization can be found here.
    This code is based on the papers:
    • M. Alkämper, S. Hilb, and A. Langer, A primal-dual adaptive finite element method for total variation minimization, Advances in Computational Mathematics, Vol. 51, No. 42, 2025. [pdf][arXiv][link]
    • S. Hilb, A. Langer, and M. Alkämper, A primal-dual finite element method for scalar and vectorial total variation minimization, Journal of Scientific Computing, Vol. 96, No. 24, 2023. [pdf] [link]

Physics-Informed Neural Networks (PINNs)

  • A Python-package for physics-informed neural networks (PINNs) based on automatic differentiation and finite differences can be found here.
    This code is based on the paper:
    • A. Langer, The ill-posed foundations of physics-informed neural networks and their finite-difference variants, arXiv preprint arXiv:2601.07017, 2026. [link]