114 citations · 649 across the 22 of their papers we have counts for
19 papers · 1 filter
Variational Model-Based Reconstruction Techniques for Multi-Patch Data in Magnetic Particle Imaging
Vladyslav Gapyak, Thomas März, Andreas Weinmann
Magnetic Particle Imaging is an emerging imaging modality through which it is possible to detect tracers containing superparamagnetic nanoparticles. The exposure of the particles t…
Smoothing splines for discontinuous signals
Martin Storath, Andreas Weinmann
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of t…
Multi-Channel Potts-Based Reconstruction for Multi-Spectral Computed Tomography
Lukas Kiefer, Stefania Petra, Martin Storath +1
We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed t…
Clothoid Fitting and Geometric Hermite Subdivision
Ulrich Reif, Andreas Weinmann
We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertice…
Non-smooth variational regularization for processing manifold-valued data
Martin Holler, Andreas Weinmann
Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations requ…
Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements -- the multivariate case
Lukas Kiefer, Martin Storath, Andreas Weinmann
Signals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics, and electrical engineering. The concrete data are often discr…
Wavelet Sparse Regularization for Manifold-Valued Data
Martin Storath, Andreas Weinmann
In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models…
Variational Regularization of Inverse Problems for Manifold-Valued Data
Martin Storath, Andreas Weinmann
In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold…
Smoothing for signals with discontinuities using higher order Mumford-Shah models
Martin Storath, Lukas Kiefer, Andreas Weinmann
Minimizing the Mumford-Shah functional is frequently used for smoothing signals or time series with discontinuities. A significant limitation of the standard Mumford-Shah model is…
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…
Total Generalized Variation for Manifold-valued Data
K. Bredies, M. Holler, M. Storath +1
In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data in a discrete setting. We provide an axiomatic appro…
Model-Based Reconstruction for Magnetic Particle Imaging in 2D and 3D
Thomas März, Andreas Weinmann
We contribute to the mathematical modeling and analysis of magnetic particle imaging which is a promising new in-vivo imaging modality. Concerning modeling, we develop a structured…
A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images
Miroslav Bačák, Ronny Bergmann, Gabriele Steidl +1
We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models we…
Exact algorithms for -TV regularization of real-valued or circle-valued signals
Martin Storath, Andreas Weinmann, Michael Unser
We consider -TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the…
A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data
Ronny Bergmann, Andreas Weinmann
In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonline…
Inpainting of Cyclic Data using First and Second Order Differences
Ronny Bergmann, Andreas Weinmann
Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restorat…
Mumford-Shah and Potts Regularization for Manifold-Valued Data with Applications to DTI and Q-Ball Imaging
Andreas Weinmann, Laurent Demaret, Martin Storath
Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving…
Second Order Differences of Cyclic Data and Applications in Variational Denoising
Ronny Bergmann, Gabriele Steidl, Friederike Laus +1
In many image and signal processing applications, as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or color image restoration in HSV or L…
Jump-sparse and sparse recovery using Potts functionals
Martin Storath, Andreas Weinmann, Laurent Demaret
We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical resul…