A direct comparison of fast 3D CGO-based algorithms for electrical impedance tomography: $ \mathbf{t^{exp}} $ and $ \mathbf{t^0} $ vs. the " $ \mathbf{t^B} $ method" on simulated and experimental data
Year: 2026
Type: article
Abstract: The inverse conductivity problem, also known as Calderon's problem, is a notoriously challenging problem. To combat the ill-posedness of the nonlinear inverse problem, strong regularization is required, and traditional variational methods are computationally expensive and highly sensitive to incorrect modeling of the forward problem. However, complex geometrical optics (CGO)-based methods are an attractive alternative due to their near real-time speed and their robustness to domain modeling errors. In this paper, we present the first numerical implementation of the nonlinear '$ \mathbf{t^B} $ method' on simulated and experimental electrode data and compare $ \mathbf{t^B} $ reconstructions to simplifications from the $ \mathbf{t^0} $ and $ \mathbf{t^{exp}} $ approximations. The computational cost of the $ \mathbf{t^B} $ method is much higher than that of the $ \mathbf{t^0} $ and $ \mathbf{t^{exp}} $ methods, without significant improvement in spatial resolution. Reconstruction quality is, however, improved across all three methods with the number of electrodes is increased.
Source: Inverse Problems and Imaging
DOI: 10.3934/ipi.2026020
Authors: Emily J. Corcoran, Sarah J. Hamilton
Institution: Marquette University
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7133206889