A semi-analytical perturbation model for diffusion tomogram reconstruction from time-resolved optical projections

This paper proposes a perturbation model for time-domain diffuse optical tomography in the flat layer transmission geometry. We derive an analytical representation of the weighting function that models the imaging operator by using the diffusion approximation of the radiative transfer equation and the perturbation theory by Born. To evaluate the weighing function for the flat layer geometry, the Green’s function of the diffusion equation for a semi-infinite scattering medium with the Robin boundary condition is used. For time-domain measurement data we use the time-resolved optical projections defined as relative disturbances in the photon fluxes, which are caused by optical inhomogeneities. To demonstrate the efficiency of the proposed model, a numerical experiment was conducted, wherein the rectangular scattering objects with two absorbing inhomogeneities and a randomly inhomogeneous component were reconstructed. Test tomograms are recovered by means of the multiplicative algebraic reconstruction technique modified by us. It is shown that nonstandard interpretation of the time-domain measurement data makes it possible to use different time-gating delays for regularization of the reconstruction procedure. To regularize the solution, we state the reconstruction problem for an augmented system of linear algebraic equations. At the recent stage of study the time-gating delays for regularization are selected empirically.