180 citations · 1.3k across the 95 of their papers we have counts for
60 papers · 1 filter
Derivative-Free iterative One-Step Reconstruction for Multispectral CT
Thomas Prohaszka, Lukas Neumann, Markus Haltmeier
Image reconstruction in Multispectral Computed Tomography (MSCT) requires solving a challenging nonlinear inverse problem, commonly tackled via iterative optimization algorithms. E…
Breaking the Resolution limit in Photoacoustic Imaging using Positivity and Sparsity
Peter Burgholzer, Johannes Bauer-Marschallinger, Mike Hettich +1
In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our obj…
Heat diffusion blurs photothermal images with increasing depth
Peter Burgholzer, Günther Mayr, Gregor Thummerer +1
In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our obj…
Sampling and resolution in sparse view photoacoustic tomography
Markus Haltmeier, Daniel Obmann, Karoline Felbermayer +2
We investigate resolution in photoacoustic tomography (PAT). Using Shannon theory, we investigate the theoretical resolution limit of sparse view PAT theoretically, and empirically…
Relaxed data-consistency for limited bandwidth photoacoustic tomography
Daniel Obmann, Markus Haltmeier
We study the effect of using weaker forms of data-fidelity terms in generalized Tikhonov regularization accounting for model uncertainties. We show that relaxed data-consistency co…
Superiorized Regularization of Inverse Problems
Aviv Gibali, Markus Haltmeier
Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regulariza…
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…
Convergence of non-linear diagonal frame filtering for regularizing inverse problems
Andrea Ebner, Markus Haltmeier
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect…
Convergence analysis of equilibrium methods for inverse problems
Daniel Obmann, Gyeongha Hwang, Markus Haltmeier
Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successfu…
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…
Plug-and-Play image reconstruction is a convergent regularization method
Andrea Ebner, Markus Haltmeier
Non-uniqueness and instability are characteristic features of image reconstruction processes. As a result, it is necessary to develop regularization methods that can be used to com…
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 systems of nonlinear ill-posed equations: II. Applications
M. Haltmeier, R. Kowar, A. Leitao +1
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem r…
Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis
M. Haltmeier, A. Leitao, O. Scherzer
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in…
Discretization of learned NETT regularization for solving inverse problems
Stephan Antholzer, Markus Haltmeier
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of…
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…
Multi-Scale Factorization of the Wave Equation with Application to Compressed Sensing Photoacoustic Tomography
Gerhard Zangerl, Markus Haltmeier
Performing a large number of spatial measurements enables high-resolution photoacoustic imaging without specific prior information. However, the acquisition of spatial measurements…
Regularization of Inverse Problems by Neural Networks
Markus Haltmeier, Linh V. Nguyen
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse probl…
Sparse aNETT for Solving Inverse Problems with Deep Learning
Daniel Obmann, Linh Nguyen, Johannes Schwab +1
We propose a sparse reconstruction framework (aNETT) for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transfo…
Data-consistent neural networks for solving nonlinear inverse problems
Yoeri E. Boink, Markus Haltmeier, Sean Holman +1
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical recons…
The conical Radon transform with vertices on triple lines
Markus Haltmeier, Sunghwan Moon
We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant at…
Deep synthesis regularization of inverse problems
Daniel Obmann, Johannes Schwab, Markus Haltmeier
Recently, a large number of efficient deep learning methods for solving inverse problems have been developed and show outstanding numerical performance. For these deep learning met…