The photon average trajectory method for One-step diffuse optical tomography: Algebraic reconstruction and postprocessing

The photon average trajectory method reduces the inverse problem of diffuse optical tomography to solution of an integral equation with integration along a curvilinear photon average trajectory. As a result, the discrete reconstruction model with the one-step inversion of a system of linear algebraic equations can be applied. For solving the system, we use the multiplicative algebraic reconstruction technique modified to improve the quality of diffusion tomograms. Space-varying restoration and methods of nonlinear color interpretation are applied for postprocessing. To study the efficiency of proposed methods, a numerical experiment is conducted, where a rectangular scattering object with circular absorbing inhomogeneities is reconstructed over optical projections simulated for the time-domain measurement technique. It is shown that our approach allows reconstructing images with quality close to that of well-designed multi-step algorithms at considerable savings of computational time.