We report what to our knowledge is a novel perturbation approach for time-resolved transmittance imaging in diffusive media, based on the diffusion approximation with extrapolated boundary conditions. The model relies on the method of Padé approximants and consists of a nonlinear approximation of time-resolved transmittance curves in the presence of an inclusion. The proposed model is intended to extend the range of applicability of perturbation models when applied to inclusions that are non-point-like. We test the model on different tissue phantoms with scattering only, absorbing only, and both scattering and absorbing inclusions. Maps of the optical properties are displayed, and the results are compared with those obtained by means of the usual linear approximation of time-resolved transmittance curves. We found that the nonlinear approach gives a better prediction for absolute values of the scattering and absorption coefficients of inclusions, when the inclusion optical properties are higher than the surrounding background. Furthermore, better-resolved spots and a reduced cross talk between the two parameters are found in the reconstructed maps. Because the range of the optical properties spanned by the considered phantoms covers the values expected for optical mammography, the application of the reported reconstruction method to in vivo images of a breast appears promising from a diagnostic viewpoint.
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