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.
Keywords: EIT, regularization, Golub-Kahan, sparsity, Krylov subspace methods
@article{M2AN_2021__55_6_2827_0,
author = {Pasha, Mirjeta and Kupis, Shyla and Ahmad, Sanwar and Khan, Taufiquar},
title = {A {Krylov} subspace type method for {Electrical} {Impedance} {Tomography}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2827--2847},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/m2an/2021057},
mrnumber = {4344861},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021057/}
}
TY - JOUR AU - Pasha, Mirjeta AU - Kupis, Shyla AU - Ahmad, Sanwar AU - Khan, Taufiquar TI - A Krylov subspace type method for Electrical Impedance Tomography JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2827 EP - 2847 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021057/ DO - 10.1051/m2an/2021057 LA - en ID - M2AN_2021__55_6_2827_0 ER -
%0 Journal Article %A Pasha, Mirjeta %A Kupis, Shyla %A Ahmad, Sanwar %A Khan, Taufiquar %T A Krylov subspace type method for Electrical Impedance Tomography %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2827-2847 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021057/ %R 10.1051/m2an/2021057 %G en %F M2AN_2021__55_6_2827_0
Pasha, Mirjeta; Kupis, Shyla; Ahmad, Sanwar; Khan, Taufiquar. A Krylov subspace type method for Electrical Impedance Tomography. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2827-2847. doi: 10.1051/m2an/2021057
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