Fast 3D Partial Boundary Data EIT Reconstructions using Direct Inversion CGO-based Methods

TL;DR

This work tackles the challenge of fast 3D Electrical Impedance Tomography (EIT) with partial boundary data by formulating two Neumann-to-Dirichlet (ND) map–based complex geometrical optics (CGO) approaches: the $t^{exp}_{ND}$ method and a Calderón–type method. Both are non-iterative and yield absolute or time-difference images in seconds, substantially faster than conventional TV and linear-difference reconstructions, while remaining robust to noise and domain-modeling errors. The authors derive the ND versions of the CGO scattering data, implement them in three–dimensional scenarios, and validate performance on rectangular-prism phantoms, a realistic head model, and an experimental stroke-mimicking tank, including cases with incorrect domain modeling. Compared with state-of-the-art methods, the CGO reconstructions achieve real-time–class speed with competitive localization under partial data, suggesting strong potential for online monitoring in clinical contexts such as stroke management and lung imaging. The results indicate that with further post-processing or learning-based augmentation, these 3D partial-boundary CGO methods could enable practical real-time imaging in settings where electrode coverage is incomplete or access is limited.

Abstract

The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets for both absolute and time-difference imaging, when large portions of the domain are inaccessible for measurement. As most medical applications of electrical impedance tomography are limited to partial boundary data, the development of partial boundary algorithms is highly desirable. While iterative schemes have been used traditionally, their high computational cost makes them cost-prohibitive for applications that need fast imaging. The proposed algorithms require no iteration and provide informative absolute or time-difference images exceptionally quickly in under 2 seconds. Reconstructions are compared to reference reconstructions from standard linear difference imaging (30 seconds) and total variation regularized absolute imaging (several minutes) The algorithms perform well under high levels of noise and incorrect domain modeling.

Figures (9)

• Figure 1: Electrode configurations
• Figure 2: True versus approximate domain modeling. In the overlays, the true mesh is red with blue electrodes, and the approximate mesh is black with green electrodes.
• Figure 3: Difference image target location from truth (in cm) using Calder'on's method. Blue, red, and magenta represent results from the 32, 28, and 20 electrode configurations, while $\times$ and $\circ$ represent results from absolute and difference images.
• Figure 4: Localization error (LE) for Calderón's method reconstructions for all three electrode configurations. The vertical dashed line indicates the last $x_2$ location covered by an electrode. Black $\times$, green $\circ$, blue $\square$, and magenta $\triangleright$ indicate LE for $0\%, 0.01\%, 0.1\%,$ and $1\%$ noise, respectively.
• Figure 5: Absolute images Calderón's method; cross-sections through the $x_3$ center of the true target. The black circle indicates the true target location. In cases with fewer electrodes, the right side is where electrodes are not present, as shown by the dashed vertical line.