Analytical representation of the sensitivity functions for high-resolution image reconstruction in parallel-plate time-domain diffuse optical tomography

The main problem in diffuse optical tomography is too low spatial resolution due to the multiple scattering of light. For solving this problem we have recently proposed a perturbation model that uses the early arriving diffuse photons for reconstructing the local disturbances of absorbing and diffusion coefficients. In the paper we develop our approach and derive an analytical representation of the sensitivity functions, which model the imaging operator, for parallel-plate transmission geometry. We first derive analytical expressions for the case of a semi-infinite scattering medium by using Green's function of the non-stationary diffusion equation and then apply these expressions to evaluate the sensitivity functions for parallel-plate transmission geometry using an original method of equivalent inverse source. The efficiency of our approach is demonstrated through a numerical experiment wherein the absorbing and scattering inhomogeneities in a rectangular scattering phantom are recovered using an original hybrid algorithm which combines the algebraic reconstruction technique with regularization via total variation norm minimization. It is shown that the transverse resolution as well as the longitudinal one can be better than 4 mm inside a 8-cm-thick phantom.