Ronny Bergmann - NTNU

About

Ronny Bergmann is Associate Professor at the Department of Mathematical Sciences since March 2021.

He was a researcher and deputy head Arbeitsgruppe Numerik partieller Differentialgleichungen (since April 2021: scoop@IWR Heidelberg), Technische Universität Chemnitz, which he joined in April 2018. Previously he worked within the Image Processing Group (since 2020: FG angew. Math.@TU Berlin), Technische Universität Kaiserslautern, where he finished his habilitation beginning of 2018. Prior to that he was a doctoral researcher and teaching assistant at the Institut für Mathematik, Universität zu Lübeck, working together with his PhD supervisor Jürgen Prestin.

For supervised projects, bachelor and master theses topics, see here.

Publications

2024

Zimmermann, Ralf; Bergmann, Ronny. (2024) Multivariate Hermite interpolation of manifold-valued data. SIAM Journal on Scientific Computing
Academic article
Bergmann, Ronny; Ferreira, Orizon P.; M. Santos, Elianderson; Souza, João Carlos O.. (2024) The Difference of Convex Algorithm on Hadamard Manifolds. Journal of Optimization Theory and Applications
Academic article

2023

Axen, Seth D.; Baran, Mateusz; Bergmann, Ronny; Rzecki, Krzysztof. (2023) Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds. ACM Transactions on Mathematical Software
Academic article
Baumgärtner, Lukas; Bergmann, Ronny; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2023) Total Generalized Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging. SIAM Journal of Imaging Sciences
Academic article

2022

Bergmann, Ronny. (2022) Manopt.jl: Optimization on Manifolds in Julia. Journal of Open Source Software (JOSS)
Academic article
Silva Louzeiro, Maurício; Bergmann, Ronny; Herzog, Roland. (2022) Fenchel Duality and a Separation Theorem on Hadamard Manifolds. SIAM Journal on Optimization
Academic article
Bergmann, Ronny; Herzog, Roland; Ortiz López, Julian; Schiela, Anton. (2022) First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints. Journal of Optimization Theory and Applications
Academic article

2021

Bergmann, Ronny; Herzog, Roland; Silva Louzeiro, Maurício; Tenbrinck, Daniel; Vidal-Núñez, José. (2021) Fenchel duality for Convex Optimization and a Primal Dual Algorithm on Riemannian Manifolds. Foundations of Computational Mathematics
Academic article

2020

Bergmann, Ronny; Herrmann, Marc; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2020) Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems. Inverse Problems
Academic article
Bergmann, Ronny; Merkert, Dennis. (2020) FFT-based homogenization on periodic anisotropic translation invariant spaces. Applied and Computational Harmonic Analysis
Academic article
Bergmann, Ronny; Herrmann, Marc; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2020) Total variation of the normal vector field as shape prior. Inverse Problems
Academic article

2019

Bergmann, Ronny; Herzog, Roland. (2019) Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds. SIAM Journal on Optimization
Academic article

2018

Bergmann, Ronny; Fitschen, Jan Henrik; Persch, Johannes; Steidl, Gabriele. (2018) Priors with coupled first and second order differences for manifold-valued image processing. Journal of Mathematical Imaging and Vision
Academic article
Bergmann, Ronny; Tenbrinck, Daniel. (2018) A graph framework for manifold-valued data. SIAM Journal of Imaging Sciences
Academic article
Bergmann, Ronny; Merkert, Dennis. (2018) A framework for FFT-based homogenization on anisotropic lattices. Computers and Mathematics with Applications
Academic article
Bergmann, Ronny; Gousenbourger, Pierre-Yves. (2018) A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve. Frontiers in Applied Mathematics and Statistics
Academic article

2017

Bergmann, Ronny; Fitschen, Jan Henrik; Persch, Johannes; Steidl, Gabriele. (2017) Iterative multiplicative filters for data labeling. International Journal of Computer Vision
Academic article

2016

Bergmann, Ronny; Persch, Johannes; Steidl, Gabriele. (2016) A parallel Douglas–Rachford algorithm for minimizing ROF-like functionals on images with values in symmetric Hadamard manifolds. SIAM Journal of Imaging Sciences
Academic article
Bačák, Miroslav; Bergmann, Ronny; Steidl, Gabriele; Weinmann, Andreas. (2016) A second order non-smooth variational model for restoring manifold-valued images. SIAM Journal on Scientific Computing
Academic article
Bergmann, Ronny; Weinmann, Andreas. (2016) A second order TV-type approach for inpainting and denoising higher dimensional combined cyclic and vector space data. Journal of Mathematical Imaging and Vision
Academic article
Bergmann, Ronny; Chan, Raymond H.; Hielscher, Ralf; Persch, Johannes; Steidl, Gabriele. (2016) Restoration of manifold-valued images by half-quadratic minimization. Inverse Problems and Imaging
Academic article

2015

Bergmann, Ronny; Prestin, Jürgen. (2015) Multivariate periodic wavelets of de la Vallée Poussin type. Journal of Fourier Analysis and Applications
Academic article

2014

Bergmann, Ronny; Laus, Friederike; Steidl, Gabriele; Weinmann, Andreas. (2014) Second order differences of cyclic data and applications in variational denoising. SIAM Journal of Imaging Sciences
Academic article

2013

Bergmann, Ronny. (2013) The fast Fourier transform and fast wavelet transform for patterns on the torus. Applied and Computational Harmonic Analysis
Academic article

Journal publications

Zimmermann, Ralf; Bergmann, Ronny. (2024) Multivariate Hermite interpolation of manifold-valued data. SIAM Journal on Scientific Computing
Academic article
Bergmann, Ronny; Ferreira, Orizon P.; M. Santos, Elianderson; Souza, João Carlos O.. (2024) The Difference of Convex Algorithm on Hadamard Manifolds. Journal of Optimization Theory and Applications
Academic article
Axen, Seth D.; Baran, Mateusz; Bergmann, Ronny; Rzecki, Krzysztof. (2023) Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds. ACM Transactions on Mathematical Software
Academic article
Baumgärtner, Lukas; Bergmann, Ronny; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2023) Total Generalized Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging. SIAM Journal of Imaging Sciences
Academic article
Bergmann, Ronny. (2022) Manopt.jl: Optimization on Manifolds in Julia. Journal of Open Source Software (JOSS)
Academic article
Silva Louzeiro, Maurício; Bergmann, Ronny; Herzog, Roland. (2022) Fenchel Duality and a Separation Theorem on Hadamard Manifolds. SIAM Journal on Optimization
Academic article
Bergmann, Ronny; Herzog, Roland; Ortiz López, Julian; Schiela, Anton. (2022) First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints. Journal of Optimization Theory and Applications
Academic article
Bergmann, Ronny; Herzog, Roland; Silva Louzeiro, Maurício; Tenbrinck, Daniel; Vidal-Núñez, José. (2021) Fenchel duality for Convex Optimization and a Primal Dual Algorithm on Riemannian Manifolds. Foundations of Computational Mathematics
Academic article
Bergmann, Ronny; Herrmann, Marc; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2020) Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems. Inverse Problems
Academic article
Bergmann, Ronny; Merkert, Dennis. (2020) FFT-based homogenization on periodic anisotropic translation invariant spaces. Applied and Computational Harmonic Analysis
Academic article
Bergmann, Ronny; Herrmann, Marc; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2020) Total variation of the normal vector field as shape prior. Inverse Problems
Academic article
Bergmann, Ronny; Herzog, Roland. (2019) Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds. SIAM Journal on Optimization
Academic article
Bergmann, Ronny; Fitschen, Jan Henrik; Persch, Johannes; Steidl, Gabriele. (2018) Priors with coupled first and second order differences for manifold-valued image processing. Journal of Mathematical Imaging and Vision
Academic article
Bergmann, Ronny; Tenbrinck, Daniel. (2018) A graph framework for manifold-valued data. SIAM Journal of Imaging Sciences
Academic article
Bergmann, Ronny; Merkert, Dennis. (2018) A framework for FFT-based homogenization on anisotropic lattices. Computers and Mathematics with Applications
Academic article
Bergmann, Ronny; Gousenbourger, Pierre-Yves. (2018) A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve. Frontiers in Applied Mathematics and Statistics
Academic article
Bergmann, Ronny; Fitschen, Jan Henrik; Persch, Johannes; Steidl, Gabriele. (2017) Iterative multiplicative filters for data labeling. International Journal of Computer Vision
Academic article
Bergmann, Ronny; Persch, Johannes; Steidl, Gabriele. (2016) A parallel Douglas–Rachford algorithm for minimizing ROF-like functionals on images with values in symmetric Hadamard manifolds. SIAM Journal of Imaging Sciences
Academic article
Bačák, Miroslav; Bergmann, Ronny; Steidl, Gabriele; Weinmann, Andreas. (2016) A second order non-smooth variational model for restoring manifold-valued images. SIAM Journal on Scientific Computing
Academic article
Bergmann, Ronny; Weinmann, Andreas. (2016) A second order TV-type approach for inpainting and denoising higher dimensional combined cyclic and vector space data. Journal of Mathematical Imaging and Vision
Academic article
Bergmann, Ronny; Chan, Raymond H.; Hielscher, Ralf; Persch, Johannes; Steidl, Gabriele. (2016) Restoration of manifold-valued images by half-quadratic minimization. Inverse Problems and Imaging
Academic article
Bergmann, Ronny; Prestin, Jürgen. (2015) Multivariate periodic wavelets of de la Vallée Poussin type. Journal of Fourier Analysis and Applications
Academic article
Bergmann, Ronny; Laus, Friederike; Steidl, Gabriele; Weinmann, Andreas. (2014) Second order differences of cyclic data and applications in variational denoising. SIAM Journal of Imaging Sciences
Academic article
Bergmann, Ronny. (2013) The fast Fourier transform and fast wavelet transform for patterns on the torus. Applied and Computational Harmonic Analysis
Academic article

Teaching

Courses

Knowledge Transfer

Quarto Extensions for the Julia Community

Quarto is an open-source scientific and technical publishing system. We propose new extensions and workflows that will help the community embrace this promising new tool and boost developers' efforts toward effective communication and reproducibility.

Manifolds in Julia – Manifolds.jl & ManifoldsBase.jl | JuliaCon 2020

Manifolds.jl provides a library of Riemannian manifolds based on the light-weight, extensible interface ManifoldsBase.jl, which can be used to implement algorithms on arbitrary manifolds.

Manopt.jl – Optimization on Riemannian Manifolds | Extended Lightning Talk | JuliaCon 2022

Manopt.jl provides a set of optimization algorithms in Julia for problems defined on a Riemannian manifold. These are implemented using the interface ManifoldsBase.jl and hence work for arbitrary manifolds from the Manifolds.jl library.

Nonsmooth, non convex Optimization on Riemannian Manifolds

Recording of a talk I gave in the Optimization in Oslo Seminar at the Department of Numerical Analysis and Scientific Computing, Simula.