55 citations · 598 across the 84 of their papers we have counts for
6 papers · 1 filter
Analysis of the Diffuse Domain Method for second order elliptic boundary value problems
Martin Burger, Ole Løseth Elvetun, Matthias Schlottbom
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental iss…
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…
Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems
Tapio Helin, Martin Burger
A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems…
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…
Maximum-A-Posteriori Estimates in Linear Inverse Problems with Log-concave Priors are Proper Bayes Estimators
Martin Burger, Felix Lucka
A frequent matter of debate in Bayesian inversion is the question, which of the two principle point-estimators, the maximum-a-posteriori (MAP) or the conditional mean (CM) estimate…