Direct numerical reconstruction of conductivities in three dimensions

TL;DR

This paper introduces a direct 3D electrical impedance tomography reconstruction algorithm using complex geometrical optics solutions and nonlinear scattering transforms, with implementation and comparison to Calderón's linear method.

Contribution

It presents a novel 3D EIT reconstruction method based on complex geometrical optics and nonlinear scattering transforms, including implementation details and comparison with existing linear techniques.

Findings

Reconstructed conductivities for test problems show the method's effectiveness.

Comparison indicates advantages over linear algorithms in certain scenarios.

Implementation details demonstrate practical feasibility.

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.