ESTIMATING ABSORPTION AND SCATTERING IN QUANTITATIVE PHOTOACOUSTIC TOMOGRAPHY WITH AN ADAPTIVE MONTE CARLO METHOD FOR LIGHT TRANSPORT

. In this work, the optical inverse problem of quantitative photoacoustic tomography is studied. Maximum a posteriori estimates for absorption and scattering are computed from absorbed energy density, and the reliability of the estimates is evaluated utilizing the Laplace's approximation. The forward operator and evaluation of the search direction in the minimization algorithm are based on the Monte Carlo method for light transport. Monte Carlo is a stochastic method where the solution of a light transport model is approximated by simulating paths of photon packets as they undergo absorption and scattering events in a scattering medium. This makes evaluation of the search direction also stochastic. In this work, we study an adaptive approach where the number of simulated photon packets on each iteration is determined by utilizing a so-called norm test. In the norm test, the variance of the gradient of the objective function is assessed and used to control the number of photon packets. The approach is studied with numerical simulations. The results show that the adaptive approach can be used to control the number of photon packets during an iterative solution of the inverse problem of quantitative photoacoustic tomography. Further, the adaptive approach can reduce the computational cost compared to a conventional approach where the number of photon packets is fixed.