Communications in Mathematical Sciences

Volume 12 (2014)

Number 2

Quantitative photoacoustic imaging in the radiative transport regime

Pages: 201 – 234

DOI: https://dx.doi.org/10.4310/CMS.2014.v12.n2.a1

Authors

Alexander V. Mamonov (Institute for Computational Engineering and Sciences, University of Texas, Austin, Tx., U.S.A.)

Kui Ren (Department of Mathematics, University of Texas, Austin, Tx., U.S.A.)

Abstract

The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and thermodynamic properties of heterogeneous media from data describing the absorbed energy distribution inside the media. There have been extensive theoretical and computational studies on the inverse problem in QPAT, although most were in the diffusive regime. We present in this work some numerical reconstruction algorithms for multi-source QPAT in the radiative transport regime with energy data collected at either single or multiple wavelengths. We show that when the medium to be probed is non-scattering, explicit reconstruction schemes can be derived to reconstruct the absorption and the Grüneisen coefficients. When data at multiple wavelengths are utilized, we can reconstruct simultaneously the absorption, scattering, and Grüneisen coefficients. We show by numerical simulations that the reconstructions are stable.

Keywords

quantitative photoacoustic tomography (QPAT), sectional photoacoustic tomography, radiative transport equation, inverse transport problem, interior data, Born approximation, iterative reconstruction

2010 Mathematics Subject Classification

49N45, 65M32, 74J25, 92C55

Published 20 September 2013