  In this paper, we describe 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/or 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 we prove the
convergence. To retrieve two coefficients simultaneously, Barzilai-Borwein (BB)
method is applied. Since the reconstruction of optical coefficients involves
the solution of original and adjoint RTEs in the framework of optimization, an
efficient solver with high accuracy is improved from~\cite{Gao}. Simulation
experiments illustrate that the improved fixed-point iterative method and the
BB method are the comparative methods for QPAT in two cases.
