Multi-source quantitative photoacoustic tomography in a diffusive regime

Photoacoustic tomography (PAT) is a novel hybrid medical imaging technique that aims to combine the large contrast of optical coefficients with the high-resolution capabilities of ultrasound. We assume that the first step of PAT, namely the reconstruction of a map of absorbed radiation from ultrasound boundary measurement, has been done. We focus on quantitative photoacoustic tomography, which aims at quantitatively reconstructing the optical coefficients from knowledge of the absorbed radiation map. We present a non-iterative procedure to reconstruct such optical coefficients, namely the diffusion and absorption coefficients, and the Gruneisen coefficient when the propagation of radiation is modeled by a second-order elliptic equation. We show that PAT measurements allow us to uniquely reconstruct only two out of the above three coefficients, even when data are collected using an arbitrary number of radiation illuminations. We present uniqueness and stability results for the reconstructions of two such parameters and demonstrate the accuracy of the reconstruction algorithm with numerical reconstructions from two-dimensional synthetic data.