Image reconstruction for random media by diffusion tomography

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Abstract
As mathematical model for the light propagation in highly scattering media, the diffusion equation for the photon density is used. The solution of the forward problem obtained by the finite element method (FEM) is compared with the analytical solution in a rectangle homogeneous domain. The application of a numerical method as the FEM allows to take into account different geometries and various embedded objects. For the inverse imaging problem two reconstruction methods are introduced acting as iterative algorithms based on the FEM forward model. As cost function the l2-norm of output flux differences for a selected combination of times, detector, and source positions is used. The effectiveness of the image reconstruction method is demonstrated by some instructive examples.

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