A shape-based reconstruction technique for DPDW data

We give an approach or directly localizing and characterizing the propertie s of a compactly supported absorption coefficient perturbation as well as c oarse scale structure of the background medium from a sparsely sampled, di use photon density wavefield. Our technique handles the problems of localiz ation and characterization simultaneously by working directly with the data , unlike traditional techniques that require two stages. We model the unkno wns as a superposition of a slowly varying perturbation on a background of unknown structure. Our model assumes that the anomaly is delineated rom the background by a smooth perimeter which is modeled as a spline curve compri sed of unknown control points. The algorithm proceeds by making small pertu rbations to the curve which are locally optimal. The result is a global, gr eedy-type optimization approach designed to enforce consistency with the da ta while requiring the solution to adhere to prior information we have conc erning the likely structure of the anomaly. At each step, the algorithm ada ptively determines the optimal weighting coefficients describing the charac teristics of both the anomaly and the background. The success of our approa ch is illustrated in two simulation examples provided for a di use photon d ensity wave problem arising in a bio-imaging application. (C) 2001 Optical Society of America.