Abstract

We present a shape-based approach to three-dimensional image reconstruction from diffuse optical data. Our approach differs from others in the literature in that we jointly reconstruct object and background characterization and localization simultaneously, rather than sequentially process for optical properties and postprocess for edges. The key to the efficiency and robustness of our algorithm is in the model we propose for the optical properties of the background and anomaly: We use a low-order parameterization of the background and another for the interior of the anomaly, and we use an ellipsoid to describe the boundary of the anomaly. This model has the effect of regularizing the inversion problem and provides a natural means of including additional physical properties if they are known a priori. A Gauss-Newton-type algorithm with line search is implemented to solve the underlying nonlinear least-squares problem and thereby determine the coefficients of the parameterizations and the descriptors of the ellipsoid. Numerical results show the effectiveness of this method.