papers

Publications (10)

math.NA2020

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…

math.OC2023

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…

math.OC2023

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…

eess.IV2025

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…

math.NA2023

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…

math.NA2021

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…

math.NA2020

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…

math.NA2025

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…

math.NA2023

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…

math.NA2019

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…