In this paper, we present the numerical reconstruction method for quantitative photoacoustic tomography (QPAT) based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and scattering coefficient of biological tissues. Given the scattering coefficient, an improved fixed-point iterative method is proposed to retrieve the absorption coefficient for its cheap computational cost. And the convergence of this method is also proved. Barzilai-Borwein (BB) method is applied to retrieve two coefficients simultaneously. Since the reconstruction of optical coefficients involves the solutions of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is developed from [15]. Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are the competitive methods for QPAT in two cases.

In this paper, we propose a hybrid method to reconstruct the absorption coefficient by fluorescence photoacoustic tomography (FPAT), which combines a squeeze iterative method (SIM) and a nonlinear optimization method. The SIM is to use two monotonic sequences to squeeze the exact coefficient, and it quickly locates near the exact coefficient. The nonlinear optimization method is utilized to attain a higher accuracy. The hybrid method inherits the advantages of each method with higher accuracy and faster convergence. The hybrid reconstruction method is also suitable for multi-measurement. Numerical experiments show that the hybrid method converges faster than the optimization method in multi-measurement case, and that the accuracy is also higher in onemeasurement case.