Journal of Biosciences and Medicines, 2013, 1, 33-36 JBM
http://dx.doi.org/10.4236/jbm.2013.12008 Published Online October 2013 (http://www.scirp.org/journal/jbm/)
Threshold strategy to improve the images reconstructed by
electrical impedance tomography
Xiaoyan Chen, Jing Zhang
College of Electronic Information and Automation, Tianjin University of Science and Technology, Tianjin, China
Received 2013
ABSTRACT
Because of the illposedness of soft field, the q uality of
EIT images is not satisfied as expected. This paper
puts forward a threshold strategy to decrease the ar-
tifacts in the reconstructed images by modifying the
solutions of inverse problem. Threshold strategy is a
kind of post processing method with merits of easy,
direct and efficient. Reconstructed by Gauss-Newton
algorithm, the simulation image’s quality is improv ed
evidently. We take two performance targets, image
reconstruction error and correlation coefficient, to
evaluate the improvement. The images and the data
show that threshold strategy is effective and achieva-
ble.
Keywords: Electrical Impedance Tomography;
Threshold Strategy; Recons truction A lgor ithm; Image
Evaluation
1. INTRODUCTION
Electrical impedance tomography (EIT) is an attractive
imaging technique which aims to estimate the interior
conductivity or resistivity distribution of an unknown
object. In EIT, an array of electrodes are attached to the
boundary of an object, safe alternating currents are in-
jected through electrodes, and the resulting voltages are
measured to reconstruct the distributions using specific
algorithms. Compared to the conventional medical im-
aging techniques, such as X-ray computerized tomogra-
phy (CT) or magnetic resonance imaging (MRI), EIT has
the advantages of low cost, no radiation and easy porta-
bility and suitable for clinical monitoring applications
[1-3]. Despite its relatively poor spatial resolution, EIT,
as a tool for imaging, has been studied for over 30 years
[4-7].
With Maxwell’s electromagnetic field theory [8], the
physical model of the sensitive field for EIT system can
be derived. Apart from the physical model in the region,
the current injection and voltages measurements on
∂Ω
are described by imposing appropriate boundary condi-
tions. The complete electrode model (CEM) [9,10] i s on e
of the most sophisticated electrode models describing the
relationship between the boundary voltages and applied
currents [11]. Considering the conductive nature of the
electrodes and the drop across the contact impedance
l
z
,
the equations describing the CEM of EIT system can be
described as follows.
( )
{ }
1
1
1
0
0 \
1,2,,
1,2,,
0
0
l
L
l
e
ll
L
l
l
L
l
l
uuee
uds IulL
u
uzV ulL
V
I
σµ
σ
σ
σ
=
=
∇⋅ ∇=

∂
=∈ ∂Ω∪∪
∂
∂
=∈ ∂Ω=
∂

∂
+=∈ ∂Ω=
∂

=


=

∫
∑
∑
n
n
n



(1)
where n is the outward pointing normal vector to
∂Ω
,
σ
is the conductivity, u is the electric potential,
l
z
is
the effective contact impedance between the
'l th
elec-
trodes and the body.
l
I
and
l
V
is the injected current
and potential at each electrodes.
This paper puts forward a threshold strategy to de-
crease the artifacts in the reconstructed images. The me-
thod is described in Section 2. The reconstructed images
are shown in Section 3. Image reconstruction error, cor-
relation coefficient and the evaluations are introduced in
Section 4. Experimentations results are completed in
Section 5.
2. METHODOLOGY
Image reconstruction in EIT is a nonlinear problem,
which aims at approximating the interior conductivity
distribution by injected electrical currents and measured
resulting boundary voltages.
Difference EIT calculates a vector of conductivity
change between the object and the reference background.

X. Y. Chen, J. Zhang / Journal of Biosciences and Medicines 1 (2013) 33-36
34
Under the assumption that only small deviations from
the reference conductivity exist, the inverse problem for
EIT can be solved for linear reconstruction accurately
and rapidly, Gauss-Newton algorithm, which has been
widely used in EIT since the late 1980s [12-14] is taken
to calculate image reconstruction matrix in our research.
The solutions in the reconstruction matrix reconstruct
the images. The artifacts in the image are caused by
some unsatisfied solutions. If a threshold is set to adjust
the value within an appropriate range, the artifacts can be
cut off sharply, spatial resolution should be improved.
Suppose, there are m pixels in a field refined by finite
element method (FEM),
i
x
is the inverse solution of
pixel i (i = 1, 2, 3

m),
P
is the threshold factor, 0 or 1,
p, q is the threshold va l ue s, which s a t isfied
min( )0max( )
ii
xq px≤≤≤ ≤
. The conditions
arg 1arg2t etbackgroundt et
σσ σ ≤≤
is under investigation. Then,
the conductivity can by modified as
0, 0,
,1,
i
ii
i ii
Pqx p
x PxxPxq or xp
= <<

′=⋅=
=≤≥

(2 )
Make the conductivity closed to that of the back-
ground zero. Only the higher values over the threshold
are kept their numerical s olution. With this modification,
the reconstruction matrix is refreshed and the artifacts o f
the images expected to be reduced.
3. RECONSTRUCTION IMAGES
The reconstructed image is refined into 12 layers and 576
elements by FEM. In simulation, we set to foreign targets
in a homogenous circle. The conductivities are set to
1
background
σ
=
,
arg 1
0.5
t et
σ =
,
arg 2
2
t et
σ =
. The recon-
struction images are shown in Figure 1. The trial-and-
error method is adopted to decide the threshold. We got
0.155, 0.18qp=−=
for GN solutions.
In Figure 1, blue blocks are the lower conductivity
targets and red blocks are the higher conductivity targets.
4. EVALUATI O NS
We elaborate two targets to characterize the quality of a
reconstructed image. Clearly, there are several criteria
proposed to evaluate the EIT systems, including hard-
ware and algorithms [15,16]. Most comments of the im-
ages are lack of objectivity. In this paper, relative errors
and the correlated coefficients of images are adopted to
evaluate the modification effects.
4.1. Relative Errors (RE)
The defi ni tion of relative errors is
RE
∗
∗
−
=xx
x
(3)
Original GN MGN
(a) (b) (c)
Figure 1. Simulation reconstruct ed images. (a ) Original images;
(b) Reconstructed images by GN; (c) Modified images by GN .
where,
∗
x
is the normalized grey vector including all
the pixels of the simulated image, while x presents that
of the reconstructed image. The smaller RE means the
higher quality of the reconstructed image.
4.2. Correlated Coefficient (CC)
Correlated coefficient (CC) is adopted to express the
related degree of the reconstructed image to the simu-
lated image, and calculated by
( )
()
( )
()
1
2
2
11
N
ii
i
NN
ii
ii
x xxx
CC
xx xx
∗
∗
=
∗
∗
= =
−−
=
−−
∑
∑∑
(4)
where,
∗
x
is the normalized grey vector including all
the pixels of the simulated image, while x presents that
of the reconstructed image.
∗
x
is the average value of

X. Y. Chen, J. Zhang / Journal of Biosciences and Medicines 1 (2013) 33-36
35
∗
x
, and
x
is the average value of x. If CC is closed to
1, the reconstructed image is similar to the fact closely.
Figure 2 shows the relative errors and correlative
coefficients of 2 - 7 subjects. The solid blue lines present
data before modifying by threshold strategy and the dot-
ted red lines present that after the modification. It is ob-
vious that the dotted red lines are all lower than the solid
blue lines in (a), which means that the thresho ld strategy
improves the image quality, while the dotted red lines are
almost above the solid blue lines in (b), which mean the
modified images are more close to the true distribution.
From Figure 2, we can draw the conclusion that the
average decrease of relative error by GN is about 18.27%,
and the average improvement of correlation coefficient
by GN is about 11.71%.
5. EXPERIMENT A TIONS AND
CONCLUSIO NS
In the experiments, we collect the data by TJU-EIT sys-
tem [17,18] which has 16 metal electrodes attached
around the boundary of a cylinder tank with 28 cm di-
ameter. Salt water is background solution，and organic
glass rods are the targets. As
saltywater rods
σσ ≥
, the thre-
shold value is the same as Fi gu re 1 . Here, GN algorithm
is accomplished. The images are shown in Figure 3 and
the performance targets are compared in Figure 4.
From above figures, the images get clearer and the ar-
tifacts are decreased obviously. The RE is decreased to
47.69%，CC is improved 11.26%.
This study proposes a threshold strategy to decrease
(a)
(b)
Figure 2. Relative errors and correlation coeffi-
cients.
(a) (b) (c)
Figure 3. Experimental re constructions. (a) Ori ginal images; (b)
Images by GN dire ctly; (c) Images by GN modified.
(a)
(b)
Figure 4. Relative error and correlation coefficient
curves of the previous and post-processing by GN
(a) The relative errors of the 3 - 6 objects, (b) The
correlation coefficients of the 3 - 6 objects.
the artifacts in the images. The images are reconstructed
by Gauss-Newton algorithm. Through trial and error tests,
the appropriate threshold conductivities are adopted to

X. Y. Chen, J. Zhang / Journal of Biosciences and Medicines 1 (2013) 33-36
36
modify the reconstructed matrix, and the modified im-
ages are achieved and evaluated through the relative er-
ror and correlation coefficient, respectively. Simulation
and experimental results show that the artifacts are re-
duced and the images are improved significantly, which
prove that the proposed approach makes significant con-
tribution in improving EIT images.
6. ACKNOWLEDGEMENTS
This work is supported by Natural Science Foundation of China (GN:
50937005) and the Natural Science Foundation of Tianjin Municipal
Science and Technology Commission (GN: 08JCYBJC03500). The
authors wish to ex press thei r sp ec ial gratitu de to P rof esso r Chaoshi Ren,
Chinese Academy o f Medical Science and Peking Un ion Medical Col-
lege Institute of Biomedical Engineering for his sincerest academic
advises on this paper.
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