  Quantitative photoacoustic tomography aims at estimating optical parameters
from photoacoustic images that are formed utilizing the photoacoustic effect
caused by the absorption of an externally introduced light pulse. This optical
parameter estimation is an ill-posed inverse problem, and thus it is sensitive
to measurement and modeling errors. In this work, we propose a novel way to
solve the inverse problem of quantitative photoacoustic tomography based on the
perturbation Monte Carlo method. Monte Carlo method for light propagation is a
stochastic approach for simulating photon trajectories in a medium with
scattering particles. It is widely accepted as an accurate method to simulate
light propagation in tissues. Furthermore, it is numerically robust and easy to
implement. Perturbation Monte Carlo maintains this robustness and enables
forming gradients for the solution of the inverse problem. We validate the
method and apply it in the framework of Bayesian inverse problems. The
simulations show that the perturbation Monte Carlo method can be used to
estimate spatial distributions of both absorption and scattering parameters
simultaneously. These estimates are qualitatively good and quantitatively
accurate also in parameter scales that are realistic for biological tissues.
