Direct numerical reconstruction of conductivities in three dimensions

Abstract

A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering transform is computed both with a Born approximation and from the forward problem for purposes of comparison. Reconstructions are computed for several test problems. A connection to Calder\'on's linear reconstruction algorithm is established, and reconstructions using both methods are compared.