114 citations · 492 across the 20 of their papers we have counts for
23 papers
Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding
Stefan Volz, Martin Storath, Andreas Weinmann
Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near…
Enhanced Low-Dose CT Image Reconstruction by Domain and Task Shifting Gaussian Denoisers
Tim Selig, Thomas März, Martin Storath +1
Computed tomography from a low radiation dose (LDCT) is challenging due to high noise in the projection data. Popular approaches for LDCT image reconstruction are two-stage methods…
Degrees-of-freedom penalized piecewise regression
Stefan Volz, Martin Storath, Andreas Weinmann
Many popular piecewise regression models rely on minimizing a cost function on the model fit with a linear penalty on the number of segments. However, this penalty does not take in…
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…
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…
Bolus arrival time estimation in dynamic contrast-enhanced magnetic resonance imaging of small animals based on spline models
Alina L. Bendinger, Charlotte Debus, Christin Glowa +3
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is used to quantify perfusion and vascular permeability. In most cases a bolus arrival time (BAT) delay exists betwee…
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…
Fast Piecewise-Affine Motion Estimation Without Segmentation
Denis Fortun, Martin Storath, Dennis Rickert +2
Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise aff…
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…
Learning Steerable Filters for Rotation Equivariant CNNs
Maurice Weiler, Fred A. Hamprecht, Martin Storath
In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) 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 learning of local image features for unsupervised texture segmentation
Martin Kiechle, Martin Storath, Andreas Weinmann +1
Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or d…
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…
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…
Disparity and Optical Flow Partitioning Using Extended Potts Priors
Xiaohao Cai, Jan Henrik Fitschen, Mila Nikolova +2
This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these probl…
Joint Image Reconstruction and Segmentation Using the Potts Model
Martin Storath, Andreas Weinmann, Jürgen Frikel +1
We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a…
Total variation regularization for manifold-valued data
Andreas Weinmann, Laurent Demaret, Martin Storath
We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals w…
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…
Signal Analysis based on Complex Wavelet Signs
Martin Storath, Laurent Demaret, Peter Massopust
We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of t…
The L1-Potts functional for robust jump-sparse reconstruction
Andreas Weinmann, Martin Storath, Laurent Demaret
We investigate the non-smooth and non-convex -Potts functional in discrete and continuous time. We show -convergence of discrete -Potts functionals towards their conti…