INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 18 (2007) 813–818 doi:10.1088/0957-0233/18/3/033
A hybrid reconstruction algorithm for
electrical impedance tomography
Li Hu
1
, Huaxiang Wang
1
, Bo Zhao
1
and Wuqiang Yang
2
1
School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072,
People’s Republic of China
2
School of Electrical and Electronic Engineering, The University of Manchester, PO Box 88,
Manchester M60 1QD, UK
E-mail: huli
tju@hotmail.com, hxwang@tju.edu.cn, zhaobotju@hotmail.com and
w.yang@manchester.ac.uk
Received 1 September 2006, in final form 19 November 2006
Published 30 January 2007
Online at stacks.iop.org/MST/18/813
Abstract
Electrical impedance tomography (EIT) is a technique for reconstructing the
conductivity distribution inside an inhomogeneous distribution by injecting
currents at the boundary of a subject and measuring the resulting changes in
voltage. A hybrid method is proposed for solving the inverse problem for
EIT, which combines the Krylov subspace and the Tikhonov regularization
for double levels of regularization to the ill-posed problem. Numerical
simulation results using the hybrid method are presented and compared to
those from truncated singular value decomposition (TSVD) regularization
and the Tikhonov regularization. Experimental results with the hybrid
method are also presented, indicating that the hybrid method can reduce the
computation time, and improve the resolution of reconstructed images with
the regularization parameter automatically chosen by the L-curve method.
Keywords: electrical impedance tomography, image reconstruction, Krylov
subspace, hybrid method
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Electrical impedance tomography (EIT) has been widely used
in three principal areas: medical imaging, industrial process
imaging and geophysical surveying (Webster 1990). The
physical model for EIT can be written as
V = U(
σ; I) = R(σ)I (1)
where V is the measured voltage vector on the electrodes
surrounding the periphery of a subject, I is the injected current
vector,
σ is the conductivity distribution in a cross section of
the subject, U(
σ; I) is the forward model mapping σ and I to
V and R(
σ) is the model mapping σ to resistance.
This model depends nonlinearly on the conductivity
σ
and linearly on the current I (Vauhkonen 1997). The aim
of image reconstruction for EIT is to obtain the conductivity
distribution
σ using the boundary voltage vector V and injected
current vector I.
Because the inverse problem is both nonlinear and ill-
posed, little noise in the measured data can cause large errors
in the estimated conductivity (Borsic 2002, Vauhkonen et al
1998). Because the measurements depend nonlinearly on
the conductivity, some nonlinear algorithm, such as the
regularized Gauss–Newton method, should be used, which
requires repeated and intensive computation. Therefore, this
is not feasible in a real time system. In principle, a small
change in conductivity can be reconstructed accurately by
considering the linearized problem (Vauhkonen 1997). A
Jacobian matrix is a linear approximation at
σ
0
of the nonlinear
model. It describes the changes in the measured voltages on
the electrodes due to small changes in conductivity of the
elements in a cross section.
In order to obtain a stable solution, regularization
techniques are adopted. Two main types of regularization
method have been widely used to solve the inverse problem.
One is categorized as the penalty methods, such as the
Tikhonov regularization, in which a penalty term is added
0957-0233/07/030813+06$30.00 © 2007 IOP Publishing Ltd Printed in the UK 813
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