activity
20072024
most citedRegularization of systems of nonlinear ill-posed equations: I. Convergence Analysis

105 citations · 252 across the 38 of their papers we have counts for

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Showing 2023Show all

15 papers · 1 filter

math.NA2023

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…

math.NA2023★ 9 cited

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…

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.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.NA2023

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…

math.NA2023

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…