Abstract

We give an approach for directly localizing and characterizing the properties of a compactly supported absorption coefficient perturbation as well as coarse scale structure of the background medium from a sparsely sampled, diffuse photon density wavefield. Our technique handles the problems of localization and characterization simultaneously by working directly with the data, unlike traditional techniques that require two stages. We model the unknowns as a superposition of a slowly varying perturbation on a background of unknown structure. Our model assumes that the anomaly is delineated from the background by a smooth perimeter which is modeled as a spline curve comprised of unknown control points. The algorithm proceeds by making small perturbations to the curve which are locally optimal. The result is a global, greedy-type optimization approach designed to enforce consistency with the data while requiring the solution to adhere to prior information we have concerning the likely structure of the anomaly. At each step, the algorithm adaptively determines the optimal weighting coefficients describing the characteristics of both the anomaly and the background. The success of our approach is illustrated in two simulation examples provided for a diffuse photon density wave problem arising in a bio-imaging application.