Abstract:
Quantitative photoacoustic tomography is an emerging imaging technique that estimates choromophore concentrations inside tissues from photoacoustic images. These images are formed by combining optical information and ultrasonic propagation that result from what is known as the photoacoustic e ect. In this thesis, we investigate the use of two inversion methods, both of which rely on inversion under the Bayesian statistical framework. The rst inversion method is a two stage inversion method where the absorption coe cient distribution is reconstructed using the data obtained as a solution of the acoustic inverse initial value problem. The second inversion method is a one stage inversion method that utilizes the linearity of the acoustic forward initial value problem in order to reconstruct the absorption coe cient distribution directly from measured acoustic wave data on the sensors. Furthermore, Bayesian approximation error modelling is applied to compensate for the modelling errors that occur in both methods. The results compare the e ectiveness of both methods as well as displaying how the modelling of the approximation errors can improve the optical reconstructions.