Imaging of scattering media by diffusion tomography: an iterative perturbation approach

This paper describes an iterative perturbation approach for imaging the absorption properties of a dense scattering medium. This method iteratively adjusts the current estimate until the calculated photon fluxes for the estimated medium match the detected readings. The inverse update in each iteration is accomplished by solving a linear perturbation equation. It is similar to the compensation theory method used in electrical impedance tomography. A comparison was made between the methods of conjugate gradient descent and projection onto convex sets for the solution of the perturbation equation. The former converges more rapidly, but can yield an inaccurate solution where the problem is underdetermined. The latter can incorporate many types of a priori information to reach a correct solution, but progresses very slowly. A multigrid progressive reconstruction technique is proposed which computes the fine details with the help of the coarse structure. It is quite effective in forcing the correct solution and reducing computation time. These methods have been used to reconstruct several inhomogeneous media containing simple structures, from steady-state reflectance data. Two sets of data are tested: one calculated according to the perturbation model, and the other using Monte Carlo methods. When the difference between the absorption distributions of the test medium and the initial estimate is localized, a single step of the perturbation approach can resolve the absorption distribution reasonably well to within five transport mean free path lengths from the surface. At greater depths, the reconstruction is less reliable.