Volume 55, Number 6, November-December 2021
|Page(s)||2827 - 2847|
|Published online||25 November 2021|
A Krylov subspace type method for Electrical Impedance Tomography
Arizona State University, Tempe, Arizona, USA
2 Clemson University Clemson, South Carolina, USA
3 Colorado State University, Fort Collins, Colorado, USA
4 University of North Carolina at Charlotte, Charlotte, North Carolina, USA
* Corresponding author: email@example.com
Accepted: 12 September 2021
Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and non-invasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface. Mathematically, the reconstruction of the internal conductivity is a severely ill-posed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspace-type method for the linear sub problem during each iteration. In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible Golub-Kahan process that provides solutions that have sparse representation. For comparison, we use a well-known modified Gauss–Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate that the Krylov subspace method is better adapted to solve the ill-posed EIT problem and results in higher resolution images and faster convergence compared to reconstructions using the modified Gauss–Newton algorithm.
Mathematics Subject Classification: 65N20
Key words: EIT / regularization / Golub-Kahan / sparsity / Krylov subspace methods
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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