Effect of Domain Shape Modeling and Measurement Errors on the 2-D D-Bar Method for EIT

Abstract

The D-bar algorithm based on Nachman's 2-D global uniqueness proof for the inverse conductivity problem (Nachman, 1996) is implemented on a chest-shaped domain. The scattering transform is computed on this chest-shaped domain using trigonometric and adjacent current patterns and the complete electrode model for the forward problem is computed with the finite element method in order to obtain simulated voltage measurements. The robustness and effectiveness of the method is demonstrated on a simulated chest with errors in input currents, output voltages, electrode placement, and domain modeling.

Direct 2-D Reconstructions of Conductivity and Permittivity From EIT Data on a Human Chest

“…Fully nonlinear reconstructions of the conductivity were computed with the 2-D D-bar method based on the 1996 uniqueness proof of A. Nachman [28], which was developed as a practical algorithm in [19]–[22], [27], [31]. A nonlinear regularization method for the algorithm was established in [22].…”

“…These are the first fully nonlinear reconstructions of human data using the D-bar method with the full scattering transform. Reconstructions of simulated and tank data using the t exp approximation on noncircular domains were computed and studied in [26], [27]. The reconstructions of the permittivity are the first direct D-bar reconstructions of permittivity from experimental data and illustrate the feasibility and potential of this method.…”

Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

“…However, when the boundary is noncircular, as in the case with the chest-shaped domain used here, we must approximate using a parameterization of the boundary for . Previous methods [40], [41] have transformed the problem to the unit disc by scaling the DN map by the maximum radial value of the noncircular domain and have produced good reconstructions. Here, as in [23], we seek to improve the reconstructions by a more accurate modeling of the boundary of the domain and thus do not scale the DN map by any radial component.…”

Direct methods for image reconstruction in electrical capacitance tomography

“…In recent years, several direct algorithms have been introduced to electrical tomography by using Calderon's method (Bikowski & Mueller, 2008;Boverman, Kao, Isaacson, & Saulnier, 2009;Cao, Xu, & Wang, 2009), the dbar method (Cao, Xu, Fan, & Wang, 2010;Isaacson, Mueller, Newell, & Siltanen, 2004;Mueller, Siltanen, & Isaacson, 2002;Murphy & Mueller, 2009), the complex geometrical optics method (Astala, Mueller, Paivarinta, & Siltanen, 2010), and the factorization method (Cao et al, 2011b;Hyv€ onen, Hakula, & Pursiainen, 2007;Hyv€ oen, 2007;Schmitt, 2009). Both the dbar method and the complex geometrical optics method originate from Calderon's method (Calderon, 2006), which is practically suitable for low-contrast material distribution (Cao et al, 2009).…”