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 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 I was a doctoral researcher and teaching assistant at the Institut für Mathematik, Universität zu Lübeck, working together with his PhD supervisor Jürgen Prestin.

Publications

2023

Baumgärtner, Lukas; Bergmann, Ronny; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2023) Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging. SIAM Journal of Imaging Sciences. volum 16 (1).
Academic article

2022

Bergmann, Ronny. (2022) Manopt.jl: Optimization on Manifolds in Julia. Journal of Open Source Software (JOSS). volum 7.
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. volum 195 (2).
Academic article
Silva Louzeiro, Maurício; Bergmann, Ronny; Herzog, Roland. (2022) Fenchel Duality and a Separation Theorem on Hadamard Manifolds. SIAM Journal on Optimization. volum 32 (2).
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. volum 21.
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. volum 36 (5).
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. volum 36 (5).
Academic article
Bergmann, Ronny; Merkert, Dennis. (2020) FFT-based homogenization on periodic anisotropic translation invariant spaces. Applied and Computational Harmonic Analysis. volum 48 (1).
Academic article

2019

Bergmann, Ronny; Herzog, Roland. (2019) Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds. SIAM Journal on Optimization. volum 29 (4).
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. volum 60 (9).
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; Merkert, Dennis. (2018) A framework for FFT-based homogenization on anisotropic lattices. Computers and Mathematics with Applications. volum 76 (1).
Academic article
Bergmann, Ronny; Tenbrinck, Daniel. (2018) A graph framework for manifold-valued data. SIAM Journal of Imaging Sciences. volum 11 (1).
Academic article

2017

Bergmann, Ronny; Fitschen, Jan Henrik; Persch, Johannes; Steidl, Gabriele. (2017) Iterative multiplicative filters for data labeling. International Journal of Computer Vision. volum 123 (3).
Academic article

2016

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. volum 38 (1).
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. volum 10 (2).
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. volum 9 (3).
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. volum 55 (3).
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. volum 7 (4).
Academic article

2013

Bergmann, Ronny. (2013) The fast Fourier transform and fast wavelet transform for patterns on the torus. Applied and Computational Harmonic Analysis. volum 35 (1).
Academic article

Journal publications

Baumgärtner, Lukas; Bergmann, Ronny; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José. (2023) Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging. SIAM Journal of Imaging Sciences. volum 16 (1).
Academic article
Bergmann, Ronny. (2022) Manopt.jl: Optimization on Manifolds in Julia. Journal of Open Source Software (JOSS). volum 7.
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. volum 195 (2).
Academic article
Silva Louzeiro, Maurício; Bergmann, Ronny; Herzog, Roland. (2022) Fenchel Duality and a Separation Theorem on Hadamard Manifolds. SIAM Journal on Optimization. volum 32 (2).
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. volum 21.
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. volum 36 (5).
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. volum 36 (5).
Academic article
Bergmann, Ronny; Merkert, Dennis. (2020) FFT-based homogenization on periodic anisotropic translation invariant spaces. Applied and Computational Harmonic Analysis. volum 48 (1).
Academic article
Bergmann, Ronny; Herzog, Roland. (2019) Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds. SIAM Journal on Optimization. volum 29 (4).
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. volum 60 (9).
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; Merkert, Dennis. (2018) A framework for FFT-based homogenization on anisotropic lattices. Computers and Mathematics with Applications. volum 76 (1).
Academic article
Bergmann, Ronny; Tenbrinck, Daniel. (2018) A graph framework for manifold-valued data. SIAM Journal of Imaging Sciences. volum 11 (1).
Academic article
Bergmann, Ronny; Fitschen, Jan Henrik; Persch, Johannes; Steidl, Gabriele. (2017) Iterative multiplicative filters for data labeling. International Journal of Computer Vision. volum 123 (3).
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. volum 38 (1).
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. volum 10 (2).
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. volum 9 (3).
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. volum 55 (3).
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. volum 7 (4).
Academic article
Bergmann, Ronny. (2013) The fast Fourier transform and fast wavelet transform for patterns on the torus. Applied and Computational Harmonic Analysis. volum 35 (1).
Academic article

Teaching

Courses

Media

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.