Analysis of the Linearized Problem of Quantitative Photoacoustic Tomography

Haltmeier, Markus; Neumann, Lukáš; Nguyen, Linh V.; Rabanser, Simon

doi:10.48550/arxiv.1702.04560

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“…The initial pressure distribution only provides qualitative information about the tissue-relevant parameters, as it is the product of the optical absorption coefficient and the spatially varying optical intensity, which again indirectly depends on the tissue parameters. Quantitative photoacoustic tomography (QPAT) addresses this issue and aims at quantitatively estimating the tissue parameters by supplementing the inversion of the acoustic wave equation with an inverse problem for light propagation (see, for example, [3,6,7,13,16,17,18,33,32,41,43,44,47,49,52,56]). Figure 1.1: Basic principles of PAT.…”

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confidence: 99%

Stochastic Proximal Gradient Algorithms for Multi-Source Quantitative Photoacoustic Tomography

Rabanser

Neumann

Haltmeier

2018

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Abstract: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.

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