Scattering and absorption transport sensitivity functions for optical tomography.

Optical tomography is modelled as an inverse problem for the time-dependent linear transport equation. We decompose the linearized residual operator of the problem into absorption and scattering transport sensitivity functions. We show that the adjoint linearized residual operator has a similar physical meaning in optical tomography as the 'backprojection' operator in x-ray tomography. In this interpretation, the geometric patterns onto which the residuals are backprojected are given by the same absorption and scattering transport sensitivity functions which decompose the forward residual operator. Moreover, the 'backtransport' procedure, which has been introduced in an earlier paper by the author, can then be interpreted as an efficient scheme for 'backprojecting' all (filtered) residuals corresponding to one source position simultaneously into the parameter space by just solving one adjoint transport problem. Numerical examples of absorption and scattering transport sensitivity functions for various situations (including applications with voids) are presented.