English

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

Numerical Analysis 2020-07-08 v1 Numerical Analysis Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.2007.03018,
  title  = {3D EIT Reconstructions from Electrode Data using Direct Inversion D-bar and Calderon Methods},
  author = {Sarah J. Hamilton and David Isaacson and Ville Kolehmainen and Peter A. Muller and Jussi Toivanen and Patrick F. Bray},
  journal= {arXiv preprint arXiv:2007.03018},
  year   = {2020}
}

Comments

29 pages, 13 figures, 6 tables

R2 v1 2026-06-23T16:53:49.377Z