Time-domain diffuse optical tomography using analytic statistical characteristics of photon trajectories

The inverse problem of diffuse optical tomography (DOT) is reduced by the method of photon average trajectories (PAT) to the solution of the integral equation integrated along the conditional mean statistical photon trajectory. The PAT bending near the flat boundary of a scattering medium is estimated analytically. These estimates are used to determine the analytic statistical characteristics of photon trajectories for the flat layer geometry. The inverse DOT problem is solved by using the multiplicative algebraic algorithm modified to improve the convergence of the iteration reconstruction process. The numerical experiment shows that the modified PAT method permits the reconstruction of near-surface optical inhomogeneities virtually without distortions.