Two-dimensional inverse problem of diffusion tomography: the approach applicable for small inclusions

A method for solving the two-dimensional inverse problems of optical diffusion tomography is proposed. The method is especially designed for the imaging of small inclusions embedded in the backgrounds of strongly scattering media. Numerical simulations show that the results are stable with respect to external noise at the boundary of the sample. The location of an inclusion is obtained with an accuracy of the order of several photon transport mean-free paths in the medium in cases both with and without noise in the scattering data used for the solution of the inverse problem.