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.
Author: | Jürgen FrikelORCiD, Markus HaltmeierORCiD |
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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 |