Bayesian Image Reconstruction in Quantitative Photoacoustic Tomography

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating chromophore concentrations inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This is a hybrid imaging problem in which the solution of one inverse problem acts as the data for another ill-posed inverse problem. In the optical reconstruction of quantitative photoacoustic tomography, the data is obtained as a solution of an acoustic inverse initial value problem. Thus, both the data and the noise are affected by the method applied to solve the acoustic inverse problem. In this paper, the noise of optical data is modelled as Gaussian distributed with mean and covariance approximated by solving several acoustic inverse initial value problems using acoustic noise samples as data. Furthermore, Bayesian approximation error modelling is applied to compensate for the modelling errors in the optical data caused by the acoustic solver. The results show that modelling of the noise statistics and the approximation errors can improve the optical reconstructions.