Quantitative photoacoustic tomography is a novel imaging method which aims to reconstruct optical parameters of an imaged target based on initial pressure distribution, which can be obtained from ultrasound measurements. In this paper, a method for reconstructing the optical parameters in a Bayesian framework is presented. In addition, evaluating the credibility of the estimates is studied. Furthermore, a Bayesian approximation error method is utilized to compensate the modeling errors caused by coarse discretization of the forward model. The reconstruction method and the reliability of the credibility estimates are investigated with two-dimensional numerical simulations. The results suggest that the Bayesian approach can be used to obtain accurate estimates of the optical parameters and the credibility estimates of these parameters. Furthermore, the Bayesian approximation error method can be used to compensate for the modeling errors caused by a coarse discretization, which can be used to reduce the computational costs of the reconstruction procedure. In addition, taking the modeling errors into account can increase the reliability of the credibility estimates.
Approximation error method for full-wave tomography