On multi-spectral quantitative photoacoustic tomography in diffusive regime

The objective of quantitative photoacoustic tomography (qPAT) is to reconstruct the diffusion, absorption and Gruneisen thermodynamic coefficients of heterogeneous media from knowledge of the interior absorbed radiation. It has been shown in Bal and Ren (2011 Inverse Problems 27 075003), based on diffusion theory, that with data acquired at one given wavelength, all three coefficients cannot be reconstructed uniquely. In this work, we study the multi-spectral qPAT problem and show that when multiple wavelength data are available, all coefficients can be reconstructed simultaneously under minor prior assumptions. Moreover, the reconstructions are shown to be very stable. We present some numerical simulations that support the theoretical results.