3D EIT Reconstructions from Electrode Data using Direct Inversion D-bar and Calderon Methods

TL;DR

This paper introduces the first 3D D-bar method implementation for electrical impedance tomography (EIT) using electrode data, demonstrating its effectiveness and comparison with Calderón and regularization methods on simulated noisy data.

Contribution

It presents the first numerical 3D D-bar reconstruction method for electrode data, extending 2D techniques to 3D and comparing its performance with Calderón and regularization methods.

Findings

3D D-bar method achieves comparable quality to Calderón method.

Method demonstrates robustness on noisy, simulated data.

Results suggest potential for real-time 3D EIT reconstructions.

Abstract

The first numerical implementation of a D-bar method in 3D using electrode data is presented. Results are compared to Calder\'on's method as well as more common TV and smoothness regularization-based methods. D-bar methods are based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. D-bar methods have shown great promise in 2D for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D D-bar and Calder\'on methods are demonstrated to provide comparable quality to their 2D CGO counterparts, and hold promise for real-time reconstructions.