Frequency-domain optical imaging of absorption and scattering distributions by a Born iterative method

We present a Born iterative method for reconstructing optical properties of turbid media by means of frequency-domain data. The approach is based on iterative solutions of a linear perturbation equation, which is derived from the integral form of the Helmholtz wave equation for photon-density waves. In each iteration the total field and the associated weight matrix are recalculated based on the previous reconstructed image. We then obtain a new estimate by solving the updated perturbation equation. The forward solution, also based on a Helmholtz equation, is obtained by a multigrid finite difference method. The inversion is carried out through a Tikhonov regularized optimization process by the conjugate gradient descent method. Using this method, we first reconstruct the distribution of the complex wave numbers in a test medium, from which the absorption and the scattering distributions are then derived. Simulation results with two-dimensional test media have shown that this method can yield quantitatively (in terms of coefficient values) as well as qualitatively (in terms of object location and shape) accurate reconstructions of absorption and scattering distributions in cases in which the first-order Born approximation cannot work well. Both full-angle and limitedangle measurement schemes have been simulated to examine the effect of the location of detectors and sources. The robustness of the algorithm to noise has also been evaluated.