Inverse scattering series in optical tomography

John C. Schotland
University of Pennsylvania


The inverse scattering problem (ISP) for diffuse waves consists of
recovering the spatially-varying absorption of the interior of a
bounded domain from measurements taken on its boundary. The problem
has been widely studied in the context of optical tomography---an
emerging biomedical imaging modality which uses near-infrared light as
a probe of tissue structure and function. More generally, diffusion of
multiply-scattered waves is a nearly universal feature of wave
propagation in random media.

The ISP in optical tomography is usually formulated as a nonlinear
optimization problem.   At present, the iterative methods which are
used to solve this problem are not well understood mathematically,
since error estimates and convergence results are not known. In this
talk we will show that, to some extent, it is possible to fill this
gap. In particular, we will study the solution to the ISP which arises
from inversion of the Born series. In previous work we have utilized
such series expansions as tools to develop fast, direct image
reconstruction algorithms. Here we characterize their convergence,
stability and reconstruction error. Numerical results which validate
the theory will be presented.

This is joint work with Shari Moskow.