55 citations · 598 across the 84 of their papers we have counts for
13 papers · 1 filter
On Optical Flow Models for Variational Motion Estimation
Martin Burger, Hendrik Dirks, Lena Frerking
The aim of this paper is to discuss and evaluate total variation based regularization methods for motion estimation, with particular focus on optical flow models. In addition to st…
A Nonlinear Variational Approach to Motion-Corrected Reconstruction of Density Images
Martin Burger, Jan Modersitzki, Sebastian Suhr
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model t…
Infimal Convolution Regularisation Functionals of BV and Spaces. The Case p
Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis +1
In this paper we analyse an infimal convolution type regularisation functional called , based on the total variation () and the $\mathrm{L}^{\in…
Nonlinear Spectral Analysis via One-homogeneous Functionals - Overview and Future Prospects
Guy Gilboa, Michael Moeller, Martin Burger
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the…
Lane formation by side-stepping
Martin Burger, Sabine Hittmeir, Helene Ranetbauer +1
In this paper we study a system of nonlinear partial differential equations, which describes the evolution of two pedestrian groups moving in opposite direction. The pedestrian dyn…
Diffuse Interface Methods for Inverse Problems: Case Study for an Elliptic Cauchy Problem
Martin Burger, Ole Loseth Elvetun, Matthias Schlottbom
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. Thi…
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…
Second-order edge-penalization in the Ambrosio-Tortorelli functional
Martin Burger, Teresa Esposito, Caterina Zeppieri
We propose and study two variants of the Ambrosio-Tortorelli functional where the first-order penalization of the edge variable is replaced by a second-order term depending on…
Infimal convolution regularisation functionals of BV and spaces. Part I: The finite case
Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis +1
We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the to…
Spectral Representations of One-Homogeneous Functionals
Martin Burger, Lina Eckardt, Guy Gilboa +1
This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or -norms. Those functi…
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…
On a Boltzmann mean field model for knowledge growth
Martin Burger, Alexander Lorz, Marie-Therese Wolfram
In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll. We discuss the underlying mathematical model, which cons…
Flow Characteristics in a Crowded Transport Model
Martin Burger, Jan-Frederik Pietschmann
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including s…