Inverse Transport Theory of Photoacoustics

Abstract

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions.

References in corpus (2)

• Thermoacoustic tomography with variable sound speed
• Time-dependent angularly averaged inverse transport

Cited by in corpus (15)

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• On Iterative Algorithms for Quantitative Photoacoustic Tomography in the Radiative Transport Regime
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• Characterizing impacts of model uncertainties in quantitative photoacoustics
• Quantitative PAT with simplified $P_N$ approximation
• Image reconstruction in quantitative photoacoustic tomography with the simplified $P_2$ approximation
• Analysis of the Linearized Problem of Quantitative Photoacoustic Tomography