Abstract

We demonstrate a fast and reasonably accurate reconstruction algorithm for optical tomography based on the propagation-backpropagation strategy. The propagation is done by solving the FEM discretization of the diffusion equation (DE) and the reconstruction is carried out through inversion of the perturbation equation. Starting with an initial estimate of the absorption(μa) and scattering coefficients(μs), the computed measurements at a number of detected points are obtained solving the DE. The difference between the experimental data and computed data for each source position is connected to a perturbation in μa and μs and inverted using direct matrix inversion to obtain a correction Δμa and Δμs' to the first estimate. The above procedure when repeated over all the sources completes one iteration in the reconstruction. We show that by dividing the reconstruction problem into a number of sub-problems, one for each source point, we are able to do a straightforward matrix inversion to quickly arrive at a correction term for absorption coefficient inhomogeneities. The resulting algorithm resembles the ART of X-ray tomography and is able to reconstruct accurately the position and extent of inhomogeneity hidden in a highly scattering background.

© 2002 Optical Society of America

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