7 papers
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…
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…