Threshold strategy to improve the images reconstructed by electrical impedance tomography

doi:10.4236/jbm.2013.12008

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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/)

OPEN ACCESS

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

Email: [email protected], [email protected]

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

the equations describing the CEM of EIT system can be

described as follows.

( )

{ }

0 \

1,2,,

uuee

uds IulL

uzV ulL

σµ

∇⋅ ∇=



∂

=∈ ∂Ω∪∪

∂

=∈ ∂Ω=

∂



∂

+=∈ ∂Ω=

∂



=



=



∫

∑



(1)

where n is the outward pointing normal vector to

∂Ω

is the conductivity, u is the electric potential,

the effective contact impedance between the

'l th

elec-

trodes and the body.

and

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

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),

is the inverse solution of

pixel i (i = 1, 2, 3



m),

is the threshold factor, 0 or 1,

p, q is the threshold va l ue s, which s a t isfied

min( )0max( )

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

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

background

arg 1

0.5

t et

arg 2

t et

. 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

∗

−

=xx

(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,

∗

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

( )

()

( )

()

x xxx

xx xx

∗

= =

−−

∑

∑∑

(4)

where,

∗

is the normalized grey vector including all

the pixels of the simulated image, while x presents that

of the reconstructed image.

∗

is the average value of

X. Y. Chen, J. Zhang / Journal of Biosciences and Medicines 1 (2013) 33-36

∗

, and

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

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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