Layer stripping: a direct numerical method for impedance imaging

An impedance imaging problem is to find the electrical conductivity and permittivity distributions inside a body from measurements made on the boundary. The following experiment is considered: a set of electric currents are applied to the surface of the body and the resulting voltages are measured on that surface. The authors describe the performance of a direct numerical method for approximating the conductivity in the interior. The algorithm proceeds via two steps: first the conductivity is found near the bounding surface of the body from the data having the highest available spatial frequency; next the boundary data on an interior surface are synthesized using a nonlinear differential equation of Riccati type. The process is then repeated, and an estimate of the conductivity is found, layer by layer. They establish the theoretical basis for the algorithm and report on numerical tests.