Reconstructing conductivities with boundary corrected D-bar method

TL;DR

This paper improves the D-bar method for electrical impedance tomography by removing the boundary constancy assumption, leading to more accurate reconstructions especially for high-contrast boundary features.

Contribution

The paper introduces a boundary correction in the D-bar method, enhancing reconstruction accuracy for conductivities with boundary features.

Findings

Improved reconstructions for high-contrast boundary conductivities.

Boundary correction reduces quantitative error.

Previous methods suffice for most medical imaging conductivities.

Abstract

The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed inverse problem and calls for a special regularized algorithm. One such algorithm, the so-called D-bar method, is improved in this work by introducing new computational steps that remove the so far necessary requirement that the conductivity should be constant near the boundary. The numerical experiments presented suggest two conclusions. First, for most conductivities arising in medical imaging, it seems the previous approach of using a best possible constant near the boundary is sufficient. Second, for conductivities that have high contrast features at the boundary, the new approach produces reconstructions with smaller quantitative error and with better visual quality.