3.5k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University Hospital Schleswig-HolsteinDE21 papers
- Universität HamburgDE14 papers
- Ludwig-Maximilians-Universität MünchenDE11 papers
- University of OxfordGB10 papers
- Hamburg University of TechnologyDE9 papers
- University Medical Center Hamburg-EppendorfDE9 papers
- Worcester Polytechnic InstituteUS9 papers
- Christian-Albrechts-Universität zu KielDE8 papers
- Heidelberg UniversityDE8 papers
- University of KaiserslauternDE8 papers
- Fraunhofer Institute for Digital MedicineDE7 papers
- Institute of Applied Mathematics and MechanicsUA7 papers
16 papers · 1 filter
An Analysis of Approximation Algorithms for Iterated Stochastic Integrals and a Julia and MATLAB Simulation Toolbox
Felix Kastner, Andreas Rößler
For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms…
Hessian Initialization Strategies for L-BFGS Solving Non-linear Inverse Problems
Hari Om Aggrawal, Jan Modersitzki
L-BFGS is the state-of-the-art optimization method for many large scale inverse problems. It has a small memory footprint and achieves superlinear convergence. The method approxima…
A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction
Gaël Bringout, Wolfgang Erb, Jürgen Frikel
We derive a new 3D model for magnetic particle imaging (MPI) that is able to incorporate realistic magnetic fields in the reconstruction process. In real MPI scanners, the generate…
High order numerical integrators for single integrand Stratonovich SDEs
David Cohen, Kristian Debrabant, Andreas Rößler
We show that applying any deterministic B-series method of order with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and w…
Functional Liftings of Vectorial Variational Problems with Laplacian Regularization
Thomas Vogt, Jan Lellmann
We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration m…
Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging
Wolfgang Erb, Andreas Weinmann, Mandy Ahlborg +10
Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response i…
A unifying theory for multivariate polynomial interpolation on general Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb
The goal of this article is to provide a general multivariate framework that synthesizes well-known non-tensorial polnomial interpolation schemes on the Padua points, the Morrow-Pa…
Measure-Valued Variational Models with Applications to Diffusion-Weighted Imaging
Thomas Vogt, Jan Lellmann
We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study w…
Fast Fourier Transforms for Spherical Gauss-Laguerre Basis Functions
Jürgen Prestin, Christian Wülker
Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type , , $L_…
Enhancing the Order of the Milstein Scheme for Stochastic Partial Differential Equations with Commutative Noise
Claudine Leonhard, Andreas Rößler
We consider a higher-order Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativity condition. A novel technique t…
Bivariate Lagrange interpolation at the node points of Lissajous curves - the degenerate case
Wolfgang Erb
In this article, we study bivariate polynomial interpolation on the node points of degenerate Lissajous figures. These node points form Chebyshev lattices of rank and are gener…
Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves
Wolfgang Erb, Christian Kaethner, Mandy Ahlborg +1
Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization…
Stability Analysis and Classification of Runge-Kutta Methods for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise
Dominique Küpper, Anne Kværnø, Andreas Rößler
The problem of solving stochastic differential-algebraic equations (SDAEs) of index one with a scalar driving Brownian motion is considered. Recently, the authors proposed a class…
Accelerated Landweber methods based on co-dilated orthogonal polynomials
Wolfgang Erb
In this article, we introduce and study accelerated Landweber methods for linear ill-posed problems obtained by an alteration of the coefficients in the three-term recurrence relat…
The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus
Ronny Bergmann
We introduce a fast Fourier transform on regular d-dimensional lattices. We investigate properties of congruence class representants, i.e. their ordering, to classify directions an…
Optimally space localized polynomials with applications in signal processing
Wolfgang Erb
For the filtering of peaks in periodic signals, we specify polynomial filters that are optimally localized in space. The space localization of functions having an expansion in term…