- INVERSE PROBLEMS Journal
- June 2009
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We seek to reconstruct an absorbing obstacle contained within the top layer of a two-layer halfspace from boundary
measurements of backscattered light. This problem is a model for
detecting early stages of cancer development in thin epithelial tissues
that reside on top of thick stromal tissues. For the direct obstacle
scattering problem, we use a combination of the discrete ordinate method
with a pseudo-spectral/finite difference method to compute numerical
solutions. For the inverse obstacle scattering problem, we use the first
Born approximation to compute an explicit solution for a thin obstacle.
Using that solution, we seek a numerical fit to the data to determine
the depth of the obstacle. Using that recovered depth, we then seek a
reconstruction of its transverse spatial distribution.