Reconstruction in optical tomography using the PN approximations

In this paper, we consider the inverse problem of reconstructing the absorption and scattering coefficients of the radiative transfer equation (RTE) from measurements of photon current transmitted through a scattering medium in the frequency domain. We consider an output least-squares formulation of this problem and derive the appropriate forward operators and their Frechet derivatives. For efficient implementation, we use the second-order form of the RTE and discuss its solution using a finite element method. The PN approximation is used to expand the radiance in spherical harmonics, which leads to a large sparse matrix system that can be efficiently solved. Examples are shown in the low-scattering case where the diffusion approximation fails.

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