• search hit 73 of 129
Back to Result List

Efficient regularization with wavelet sparsity constraints in photoacoustic tomography

  • In this paper, we consider the reconstruction problem of photoacoustic tomography (PAT) with a flat observation surface. We develop a direct reconstruction method that employs regularization with wavelet sparsity constraints. To that end, we derive a wavelet-vaguelette decomposition (WVD) for the PAT forward operator and a corresponding explicit reconstruction formula in the case of exact data. In the case of noisy data, we combine the WVD reconstruction formula with soft-thresholding, which yields a spatially adaptive estimation method. We demonstrate that our method is statistically optimal for white random noise if the unknown function is assumed to lie in any Besov-ball. We present generalizations of this approach and, in particular, we discuss the combination of PAT-vaguelette soft-thresholding with a total variation (TV) prior. We also provide an efficient implementation of the PAT-vaguelette transform that leads to fast image reconstruction algorithms supported by numerical results.

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Metadaten
Author:Jürgen FrikelORCiD, Markus HaltmeierORCiD
DOI:https://doi.org/10.1088/1361-6420/aaa0ac
Parent Title (English):Inverse Problems
Document Type:Article
Language:English
Year of first Publication:2018
Release Date:2022/03/18
Tag:Image reconstruction; photoacoustic tomography; sparsity constraints; variational regularization; wavelet-vaguelette decomposition
Volume:34
Issue:2
Article Number:024006
First Page:1
Last Page:28
Note:
Corresponding authors: Jürgen Frikel and Markus Haltmeier
Institutes:Fakultät Informatik und Mathematik
Begutachtungsstatus:peer-reviewed
research focus:Information und Kommunikation
OpenAccess Publikationsweg:Hybrid Open Access - OA-Veröffentlichung in einer Subskriptionszeitschrift/-medium
Corresponding author der OTH Regensburg
Licence (English):Creative Commons - CC BY - Namensnennung 3.0 International