114 citations · 188 across the 17 of their papers we have counts for
10 papers · 1 filter
Data-proximal null-space networks for inverse problems
Simon Göppel, Jürgen Frikel, Markus Haltmeier
Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established…
Translation invariant diagonal frame decomposition for the Radon transform
Simon Göppel, Markus Haltmeier, Jürgen Frikel
In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD)…
Data-proximal complementary -TV reconstruction for limited data CT
Simon Göppel, Jürgen Frikel, Markus Haltmeier
In a number of tomographic applications, data cannot be fully acquired, resulting in a severely underdetermined image reconstruction. In such cases, conventional methods lead to re…
Translation invariant diagonal frame decomposition of inverse problems and their regularization
Simon Göppel, Jürgen Frikel, Markus Haltmeier
Solving inverse problems is central to a variety of important applications, such as biomedical image reconstruction and non-destructive testing. These problems are characterized by…
Combining reconstruction and edge detection in computed tomography
Jürgen Frikel, Simon Göppel, Markus Haltmeier
We present two methods that combine image reconstruction and edge detection in computed tomography (CT) scans. Our first method is as an extension of the prominent filtered backpro…
Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition
Andrea Ebner, Jürgen Frikel, Dirk Lorenz +2
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to…
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…
Sparse regularization of inverse problems by operator-adapted frame thresholding
Jürgen Frikel, Markus Haltmeier
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allow…
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…
Sparse regularization in limited angle tomography
Jürgen Frikel
We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron…