Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium

With applications in medical diagnosis in mind we apply the theory of diffraction tomography to diffuse photon density waves in a random medium. We consider the two-and-a-half-dimensional (2.5D) problem in which a two-dimensional (2D) object is illuminated by diffuse photon density waves from a point source. Both the forward problem and the inverse problem are discussed, and a reconstruction algorithm based on the weak-scattering approximation is presented together with computer simulations.