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.
Highlights
Photoacoustic tomography (PAT) is an emerging imaging modality, which combines the benefits of pure ultrasound imaging with those of pure optical tomography; see [1,2]
We propose the following instances of the stochastic proximal gradient method for Quantitative photoacoustic tomography (QPAT) based on the multilinear formulation (35)
Standard formulation of QPAT (19): We assume that the scattering coefficient is known and we restrict ourself to reconstructing the absorption coefficient
Summary
Photoacoustic tomography (PAT) is an emerging imaging modality, which combines the benefits of pure ultrasound imaging (high resolution) with those of pure optical tomography (high contrast); see [1,2]. A fraction of the optical energy is absorbed inside the sample, which causes thermal heating, expansion, and a subsequent acoustic pressure wave depending on the interior absorbing structure of the sample. The acoustic pressure is measured outside of the sample and used to reconstruct an image of the interior. One important reconstruction problem in PAT is recovering the initial pressure distribution (see, for example, [3,4,5,6,7,8,9,10]). 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, [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26])
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