Inverse Transport Theory of Photoacoustics

TL;DR

This paper develops an inverse transport theory framework for photoacoustic tomography, enabling the reconstruction of optical parameters like attenuation and scattering coefficients, including anisotropic scattering, from internal thermal energy measurements.

Contribution

It introduces a novel inverse transport approach with internal measurements to recover detailed optical parameters in photoacoustic imaging, including anisotropic scattering coefficients.

Findings

Reconstruction of attenuation and scattering coefficients from thermal energy data.

Ability to recover anisotropic scattering parameters such as the Henyey-Greenstein g coefficient.

Derivation of stability estimates for the inverse problem.

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.