55 citations · 598 across the 84 of their papers we have counts for
32 papers · 1 filter
Convergent Data-driven Regularizations for CT Reconstruction
Samira Kabri, Alexander Auras, Danilo Riccio +4
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerize…
Gradient Flows and Nonlinear Power Methods for the Computation of Nonlinear Eigenfunctions
Leon Bungert, Martin Burger
This chapter describes how gradient flows and nonlinear power methods in Banach spaces can be used to solve nonlinear eigenvector-dependent eigenvalue problems, and how convergence…
Sequentially optimized projections in X-ray imaging
Martin Burger, Andreas Hauptmann, Tapio Helin +2
This work applies Bayesian experimental design to selecting optimal projection geometries in (discretized) parallel beam X-ray tomography assuming the prior and the additive noise…
Variational regularisation for inverse problems with imperfect forward operators and general noise models
Leon Bungert, Martin Burger, Yury Korolev +1
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lat…
Total Variation Regularisation with Spatially Variable Lipschitz Constraints
Martin Burger, Yury Korolev, Simone Parisotto +1
We introduce a first order Total Variation type regulariser that decomposes a function into a part with a given Lipschitz constant (which is also allowed to vary spatially) and a j…
A total variation based regularizer promoting piecewise-Lipschitz reconstructions
Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb +1
We introduce a new regularizer in the total variation family that promotes reconstructions with a given Lipschitz constant (which can also vary spatially). We prove regularizing pr…
Variational Graph Methods for Efficient Point Cloud Sparsification
Daniel Tenbrinck, Fjedor Gaede, Martin Burger
In recent years new application areas have emerged in which one aims to capture the geometry of objects by means of three-dimensional point clouds. Often the obtained data consist…
Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
Leon Bungert, Martin Burger, Daniel Tenbrinck
In this work we investigate the computation of nonlinear eigenfunctions via the extinction profiles of gradient flows. We analyze a scheme that recursively subtracts such eigenfunc…
Convergence rates and structure of solutions of inverse problems with imperfect forward models
Martin Burger, Yury Korolev, Julian Rasch
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem y…
The Inverse Problem of Magnetorelaxometry Imaging
Lea Föcke, Daniel Baumgarten, Martin Burger
The aim of this paper is to provide a solid mathematical discussion of the inverse problem in Magnetorelaxometry Imaging (MRXI), a currently developed technique for quantitative bi…
Unified Models for Second-Order TV-Type Regularisation in Imaging - A New Perspective Based on Vector Operators
Eva-Maria Brinkmann, Martin Burger, Joana Sarah Grah
We introduce a novel regulariser based on the natural vector field operations gradient, divergence, curl and shear. For suitable choices of the weighting parameters contained in ou…
Modern Regularization Methods for Inverse Problems
Martin Benning, Martin Burger
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feas…
Dynamic MRI Reconstruction from Undersampled Data with an Anatomical Prescan
Julian Rasch, Ville Kolehmainen, Riikka Nivajärvi +4
The goal of dynamic magnetic resonance imaging (dynamic MRI) is to visualize tissue properties and their local changes over time that are traceable in the MR signal. We propose a n…
Dynamic SPECT reconstruction with temporal edge correlation
Qiaoqiao Ding, Martin Burger, Xiaoqun Zhang
In dynamic imaging, a key challenge is to reconstruct image sequences with high temporal resolution from strong undersampling projections due to a relatively slow data acquisition…
A Variational Reconstruction Method for Undersampled Dynamic X-ray Tomography based on Physical Motion Models
Martin Burger, Hendrik Dirks, Lena Frerking +3
In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use r…
Joint Reconstruction via Coupled Bregman Iterations with Applications to PET-MR Imaging
Julian Rasch, Eva-Maria Brinkmann, Martin Burger
Joint reconstruction has recently attracted a lot of attention, especially in the field of medical multi-modality imaging such as PET-MRI. Most of the developed methods rely on the…
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…
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…
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…
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…