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

• Main Authors: Hamilton, Sarah J, Isaacson, David, Kolehmainen, Ville, Muller, Peter A, Toivanen, Jussi, Bray, Patrick F
• Format: Journal Article
• Language: English
• Published: 06-07-2020
• Subjects: Computer Science - Numerical Analysis; Mathematics - Analysis of PDEs; Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.2007.03018

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.