Publications (10)
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…
Convergence analysis of critical point regularization with non-convex regularizers
Daniel Obmann, Markus Haltmeier
One of the key assumptions in the stability and convergence analysis of variational regularization is the ability of finding global minimizers. However, such an assumption is often…
Convergence rates for critical point regularization
Daniel Obmann, Markus Haltmeier
Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use o…
Error correcting 2D-3D cascaded network for myocardial infarct scar segmentation on late gadolinium enhancement cardiac magnetic resonance images
Matthias Schwab, Mathias Pamminger, Christian Kremser +3
Late gadolinium enhancement (LGE) cardiac magnetic resonance (CMR) imaging is considered the in vivo reference standard for assessing infarct size (IS) and microvascular obstructio…
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…
Augmented NETT Regularization of Inverse Problems
Daniel Obmann, Linh Nguyen, Johannes Schwab +1
We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a…
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…
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…
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…
Sparse synthesis regularization with deep neural networks
Daniel Obmann, Johannes Schwab, Markus Haltmeier
We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an…