55 citations · 598 across the 84 of their papers we have counts for
13 papers · 1 filter
Controlling a self-organizing system of individuals guided by a few external agents -- particle description and mean-field limit
Martin Burger, René Pinnau, Andreas Roth +2
Optimal control of large particle systems with collective dynamics by few agents is a subject of high practical importance (e.g. in evacuation dynamics), but still limited mathemat…
Pattern formation of a nonlocal, anisotropic interaction model
Martin Burger, Bertram Düring, Lisa Maria Kreusser +2
We consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of…
On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion
Judith Berendsen, Martin Burger, Jan-Frederik Pietschmann
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffus…
Mathematical Imaging Methods for Mitosis Analysis in Live-Cell Phase Contrast Microscopy
Joana Sarah Grah, Jennifer Alison Harrington, Siang Boon Koh +5
In this paper we propose a workflow to detect and track mitotic cells in time-lapse microscopy image sequences. In order to avoid the requirement for cell lines expressing fluoresc…
Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems
Byung-Woo Hong, Ja-Keoung Koo, Hendrik Dirks +1
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including…
Bregman Cost for Non-Gaussian Noise
Martin Burger, Yiqiu Dong, Federica Sciacchitano
One of the tasks of the Bayesian inverse problem is to find a good estimate based on the posterior probability density. The most common point estimators are the conditional mean (C…
Cross-diffusion systems with excluded volume effects and asymptotic gradient flows
Maria Bruna, Martin Burger, Helene Ranetbauer +1
In this paper we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived by Bruna and Chapman from a stochastic system of interacting…
A Variational Model for Joint Motion Estimation and Image Reconstruction
Martin Burger, Hendrik Dirks, Carola-Bibiane Schönlieb
The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eul…
Simultaneous Reconstruction and Segmentation for Dynamic SPECT Imaging
Martin Burger, Carolin Rossmanith, Xiaoqun Zhang
This work deals with the reconstruction of dynamic images that incorporate characteristic dynamics in certain subregions, as arising for the kinetics of many tracers in emission to…
Bias-Reduction in Variational Regularization
Eva-Maria Brinkmann, Martin Burger, Julian Rasch +1
The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a…
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
Martin Burger, Alexander Lorz, Marie-Therese Wolfram
In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either i…
Large Noise in Variational Regularization
Martin Burger, Tapio Helin, Hanne Kekkonen
In this paper we consider variational regularization methods for inverse problems with large noise that is in general unbounded in the image space of the forward operator. We intro…
Spectral Decompositions using One-Homogeneous Functionals
Martin Burger, Guy Gilboa, Michael Moeller +2
This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral…