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Multiple-source quantitative photoacoustic tomography

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 ultrasounds. We assume that the first step of PAT, namely the reconstruction of a map of absorbed radiation from boundary ultrasound measurement, is done. We focus on quantitative photoacoustic tomography (QPAT), which aims at quantitatively reconstructing optical coefficients from knowledge of the absorbed radiation map. We present a non-iterative procedure to reconstruct optical coefficients -namely the diffusion and absorption coefficientsand the Grüneisen coefficient in photoacoustic tomography (PAT) when the propagation of radiation is modeled by a second-order elliptic equation. We show that PAT measurements at one given light frequency allow us to unique reconstruct only two out of the above three coefficients even for an arbitrary number of radiation illuminations. We present uniqueness and stability results and demonstrate the accuracy of the reconstruction algorithm on two-dimensional synthetic data.