Born type iterative method for imaging of heterogeneous scattering media and its application to simulated breast tissue

In this paper, we present a Born-Type iterative algorithm for reconstruction of absorption and diffusion coefficient distributions of a heterogeneous scattering medium. This method is derived based on the integral form of the diffusion equation for the photon flux. It takes into account the nonlinear nature of the problem by using an iterative perturbation approach. Within each iteration, the forward problem (update of the total field and Green's function) is solved by the finite element method (FEM), and the inverse problem (update of the medium properties) is obtained by a regularized least squares method. This method has been used to reconstruct 'pathologies' embedded in an inhomogeneous test medium simulating a normal female breast from frequency domain data. The test medium is constructed by assigning optical coefficients according to an MR derived anatomical map. Our simulation results show that the algorithm is computationally practical and can yield qualitatively and quantitatively correct absorption and scattering distributions of embedded objects from simulated data with up to 5% additive noise in the simulated measurement data.