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Open AccessFeature PaperArticle

Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic Tomography

1
Department of Mathematics, University of Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria
2
Institute of Basic Sciences in Engineering Science, University of Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(2), 121; https://doi.org/10.3390/e20020121
Received: 13 December 2017 / Revised: 22 January 2018 / Accepted: 4 February 2018 / Published: 11 February 2018
(This article belongs to the Special Issue Probabilistic Methods for Inverse Problems)
The development of accurate and efficient image reconstruction algorithms is a central aspect of quantitative photoacoustic tomography (QPAT). In this paper, we address this issues for multi-source QPAT using the radiative transfer equation (RTE) as accurate model for light transport. The tissue parameters are jointly reconstructed from the acoustical data measured for each of the applied sources. We develop stochastic proximal gradient methods for multi-source QPAT, which are more efficient than standard proximal gradient methods in which a single iterative update has complexity proportional to the number applies sources. Additionally, we introduce a completely new formulation of QPAT as multilinear (MULL) inverse problem which avoids explicitly solving the RTE. The MULL formulation of QPAT is again addressed with stochastic proximal gradient methods. Numerical results for both approaches are presented. Besides the introduction of stochastic proximal gradient algorithms to QPAT, we consider the new MULL formulation of QPAT as main contribution of this paper. View Full-Text
Keywords: photoacoustic tomography; image reconstruction; radiative transfer equation; multilinear inverse problem; limited view; stochastic gradient method; limited data; Dykstra algorithm photoacoustic tomography; image reconstruction; radiative transfer equation; multilinear inverse problem; limited view; stochastic gradient method; limited data; Dykstra algorithm
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Rabanser, S.; Neumann, L.; Haltmeier, M. Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic Tomography. Entropy 2018, 20, 121.

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