Noninvasive cross section reconstruction with tranport theory constraints
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We consider the inverse problem of identifying the spatially variable absorption and scattering properties of a medium by measuring the exiting radiation when the body is actively interrogated. We formulate this inverse problem as a PDE-constrained optimization problem and solve it iteratively with Newton's method. The constraint is given by the radiative transport equation for neutral particles. Two examples are considered. The first is a dual inclusion domain with no scattering. This problem explores the convergence patterns of the method. The second problem is a central inclusion problem with scattering. This problem explores the optical thickness limit of the method. This optical thickness was determined to be 2-3 mean free paths.
