Optical imaging: three-dimensional approximation and perturbation approaches for time-domain data.

The reconstruction method presented here is based on diffusion approximation for light propagation in turbid media and on a minimization strategy for the output-least-squares problem. A perturbation approach is introduced for the optical properties. Here we can strongly reduce the number of free variables of the inverse problem by exploiting a priori information such as the search for single inhomogeneities within a relatively homogeneous object, a typical situation for breast cancer detection. We achieve higher accuracy and a considerable reduction in computational effort by solving a parabolic differential equation for a perturbation density, i.e., the difference between the photon density in an inhomogeneous object and the density in the homogeneous case being given by an analytic expression. The calculations are performed by a two-dimensional finite-element-method algorithm. However, as a time-dependent correction factor is applied, the three-dimensional situation is well approximated. The method was successfully tested by use of the University of Pennsylvania standard data set. Data noise was generated and taken into account in a modified data set. The influence of different noise on the reconstruction results is discussed.