55 citations · 598 across the 84 of their papers we have counts for
16 papers · 1 filter
Boltzmann mean-field game model for knowledge growth: limits to learning and general utilities
Martin Burger, Laura Kanzler, Marie-Therese Wolfram
In this paper we investigate a generalisation of a Boltzmann mean field game (BMFG) for knowledge growth, originally introduced by the economists Lucas and Moll. In BMFG the evolut…
Mean-field optimal control for biological pattern formation
Martin Burger, Lisa Maria Kreusser, Claudia Totzeck
We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probabilit…
Adaptive Superresolution in Deconvolution of Sparse Peaks
Alexandra Koulouri, Pia Heins, Martin Burger
The aim of this paper is to investigate superresolution in deconvolution driven by sparsity priors. The observed signal is a convolution of an original signal with a continuous ker…
An entropic Landweber method for linear ill-posed problems
Martin Burger, Elena Resmerita, Martin Benning
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for…
Data assimilation in price formation
Martin Burger, Jan-Frederik Pietschmann, Marie-Therese Wolfram
We consider the problem of estimating the density of buyers and vendors in a nonlinear parabolic price formation model using measurements of the price and the transaction rate. Our…
Instantaneous control of interacting particle systems in the mean-field limit
Martin Burger, Rene Pinnau, Claudia Totzeck +2
Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instant…
Reconstruction Methods in THz Single-pixel Imaging
Martin Burger, Lea Föcke, Lukas Nickel +2
The aim of this paper is to discuss some advanced aspects of image reconstruction in single-pixel cameras, focusing in particular on detectors in the THz regime. We discuss the rec…
Mean-field optimal control and optimality conditions in the space of probability measures
Martin Burger, René Pinnau, Claudia Totzeck +1
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordi…
Solution Paths of Variational Regularization Methods for Inverse Problems
Leon Bungert, Martin Burger
We consider a family of variational regularization functionals for a generic inverse problem, where the data fidelity and regularization term are given by powers of a Hilbert norm…
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…
Bregman Distances in Inverse Problems and Partial Differential Equation
Martin Burger
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in…
Regularization with Sparse Vector Fields: From Image Compression to TV-type Reconstruction
Eva-Maria Brinkmann, Martin Burger, Joana Grah
This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential f…
First order algorithms in variational image processing
Martin Burger, Alex Sawatzky, Gabriele Steidl
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, i…
Towards Dynamic PET Reconstruction under Flow Conditions: Parameter Identification in a PDE Model
Louise Reips, Martin Burger, Ralf Engbers
The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in p…
Locally Sparse Reconstruction Using the -Norm
Pia Heins, Michael Moeller, Martin Burger
This paper discusses the incorporation of local sparsity information, e.g. in each pixel of an image, via minimization of the -norm. We discuss the basic propertie…
Exact Relaxation for Classes of Minimization Problems with Binary Constraints
Martin Burger, Yiqiu Dong, Michael Hintermüller
Relying on the co-area formula, an exact relaxation framework for minimizing objectives involving the total variation of a binary valued function (of bounded variation) is presente…