Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection 11
Fig. 3. Antenna array and tumor configuration
5. Evaluation of the performance of the frequency domain skin removal in
comparison with other methods
The present section applies the frequency domain skin removal method described in section 4
in different scenarios and compares its performance with other methods. The focus in the first
part is more on details of applying the formulation provided in Section 4 on a simplified breast
model. The second part will apply the method in a more realistic scenario and compares the
results with the other methods.
5.1 Simplified Breast Model
As discussed in Section 4, the backscattered signal of a UWB pulse is the summation of some
harmonic terms. The number of these terms depend on the number of scattering points and
the multiple scattering effect. Each harmonic term consists of a complex exponential and a
coefficient. The argument of this complex exponential is the pole of the hypothetical system
mentioned in Section 4. By removing the poles corresponding to the skin reflection from the
frequency domain signal, all the skin related information will be removed from time domain.
The process is as follows.
The received signals are first converted into frequency domain using Fast Fourier Transform
(FFT) algorithm. The frequency domain signals are then processed to extract the model
parameters stated in the previous section. Among these parameters, a
i
s are directly related
to the amplitudes of each of the backscattered pulses. This can be explained as follows. In
Equation (13), a
i
is a complex coefficient which can be written as |a
i
|e
jθ
i
where θ

However, the amplitude of the pulse backscattered from the tumor is much smaller than the
skin backscatter. Hence, a threshold could be defined to remove poles with dominant a
i
values
from the frequency response of the signal. Removing the poles over the stated threshold
ensures that only the poles corresponding to the skin will be removed from the signal. This
will remove the skin effect both in the early time and the late time responses as the elimination
in frequency domain will affect the whole time domain signal. Hence, the tumor reflection will
347
Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection
12 Will-be-set-by-IN-TECH
be preserved without the skin late time response interference in the signal. After removing
the skin related poles, the frequency domain signal is reconstructed using the mathematical
model (13) and then converted back into the time domain using the inverse-FFT algorithm.
Hence, the reconstructed signal will only contain contributions from the tumor and clutter.
Clutter will be rejected later using confocal imaging algorithm described in Section 1. We will
Ant. No. x y z Ant. No. x y z
1 35.71 0 35 13 -35.71 0 35
2 34.50 10.24 35 14 -34.50 -10.24 35
3 30.93 17.86 35 15 -30.93 -17.86 35
4 25.26 26.26 35 16 -25.26 -26.26 35
5 17.86 30.93 35 17 -17.86 -30.93 35
6 9.24 35.50 35 18 -9.24 -35.50 35
7 0 35.71 35 19 0 -35.71 35
8 -9.24 35.50 35 20 9.24 -35.50 35
9 -17.86 30.93 35 21 17.86 -30.93 35
10 -25.50 26.26 35 22 25.26 -26.26 35
11 -30.93 17.86 35 23 30.93 -17.86 35
12 -34.50 10.24 35 24 34.50 -10.24 35
Table 1. Antenna Arrangement

2 4 6 8 10 12 14
x 10
9
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Frequency(GHz)
Voltage(v)
(b) Frequency response of the signal received in
channel 1
Fig. 4. Signal received in channel 1 and its frequency response
348
Novel Applications of the UWB Technologies
Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection 13
skin reflects the largest energy among the reflectors in the breast medium, the high energy
dominant poles in the frequency domain will correspond to the skin backscatter. Hence a
threshold may be used to remove these dominant poles. The threshold is defined based on
the ratio of the backscattered energies of the skin to the tumor and is obtained as follows.
We fix the threshold value a little higher than the ratio of the largest possible peak tumor to
the skin response times the maximum reflection coefficient value a
i
. The maximum reflection
coefficient corresponds to the largest scatterer which is the skin surface. Hence, by removing
all the poles with a

little larger than 0.21% of the largest reflection coefficient (a
max
) and removing all the poles
with a
i
values larger than this threshold from early time response we ensure that all the
reflections larger than the tumor reflection is removed from the signal. This would be true
in all other cases as we chose the largest possible tumor response to define the threshold.
Here, we chose 0.0025
× the largest reflection coefficient as the threshold value. The poles
extracted from the signal in channel 1 are shown in Table 4; Eliminated poles are indicated by
a’
∗
’.
349
Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection
14 Will-be-set-by-IN-TECH
−50 −40 −30 −20 −10 0 10 20 30 40 50
−50
−40
−30
−20
−10
0
10
20
30
40
50
Fig. 5. Confocal imaging of the breast after removing the skin reflection

to the heterogeneity of the breast tissue has significant effect on the effectiveness of the skin
subtraction methods. In the averaging based methods, the averaged clutter from all other
350
Novel Applications of the UWB Technologies
Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection 15
1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2
x 10
−9
−4
−3
−2
−1
0
1
2
3
4
x 10
−4
Time(ns)
Voltage(v)
Fig. 7. The late time response of the reconstructed signal (line with dots) vs. the original
signal (solid)
Pole No. Reflection Coefficient Pole No. Reflection Coefficient
1 0.006030024 16 0.000576253
2 *0.330168871 17 0.000817322
3 *2.769236715 18 0.001800899
4 *8.978906551 19 0.003023339
5 *17.21322261 (MAX) 20 0.002570893
6 *16.81465757 21 0.000965909

tissue(source:(Kosmas & Rappaport, 2005))
Fig. 9. 3D Model Constructed based on MRI image, shaded region shows the scanning area
Region x y z 
r
Region x y z 
r
A 0 0 17 5.3 E 16 10 4 4.8
B -25 0.9 22 5.2 F 11 -9 11 5
C -28 26 5 4.8 G -36 -25 5.5 5
D 4 27 7 4.8 H 27 4.7 22 5.2
Table 5. Dielectric region centers (mm)
In this model, the skin layer thickness is set as 2mm. The antenna placement, physical
parameters of the normal breast tissue and tumor are set as described in the previous section.
As for the clutter regions, dielectric values are obtained from the MRI image as stated above.
These values are given in Table 5.
The skin reflection is removed from the simulated backscattered signals using all three
methods: frequency domain approach, averaging and weighted average filter to compare
the performance of these methods. A 2D image of the breast is formed by applying confocal
imaging process on the processed signals. The resulting images from the three methods are
shown in Figure 10. Due to the symmetry of the tumor location to the antenna elements in the
array, the tumor response is totally eliminated from the image processed by averaging and
filtering methods. This is because, the tumor response will add coherently in the averaging
process (due to the symmetry) and hence will appear in the average signal. Hence, subtracting
the average removes the tumor backscatter as well as the skin backscatter. However, in
frequency domain approach, each signal is processed separately and no other data is added
352
Novel Applications of the UWB Technologies
Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection 17
−50 −40 −30 −20 −10 0 10 20 30 40 50
−50

0
10
20
30
40
50
(c) Pole Removal
Fig. 10. Breast images using three skin subtraction methods: Averaging(a), Weighted
Average(b), Pole removal(c)
to or subtracted from the signal, the tumor signature remains intact. This is confirmed in
Figure 10. As seen in the figure, the tumor is detected at the central axis of the breast.
To compare the performance of the three methods in general case, the tumor is located in off
center coordinates (x = 35 , y = 0, z = 15). The other parameters of the model are the same as
the previous model.
Again, the skin reflection is removed using the three mentioned methods. The results are
shown in Figure 11.
As the figure reveals, all three methods have eliminated the skin effect and the tumor is
detected in the resulting image. To further evaluate the performance of the skin removal
methods, the peak Tumor to Clutter Ratio (TCR) for the three methods is compared in Table 6.
As seen in the table, the tumor to clutter ratio is the highest for frequency domain approach
Skin-Removal Method TCR
Pole-Removal 3.831
Weighted Average 2.082
Averaging 1.837
Table 6. Tumor to Clutter Ratio (TCR)
353
Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection
18 Will-be-set-by-IN-TECH
−50 −40 −30 −20 −10 0 10 20 30 40 50
−50

10
20
30
40
50
(c) Pole Removal
Fig. 11. Tumor at: x = 35,y=0,z=15(mm), Averaging(a), Weighted Average(b), Pole
removal(c)
and is the lowest for simple averaging. This is expected since pole removal method processes
each signal individually unlike the other two methods which add clutter from other signals
and degrade the tumor reflection.
6. Conclusion
The high contrast in the dielectric value of the skin relative to the normal breast tissue and
air produces a strong backscatter in UWB breast cancer detection method. Such strong
backscatter can totally mask the tumor reflection and hence has to be removed from the
signal. Currently, two methods are used in practice to remove skin reflection. Both methods
exploit the similarity of the skin reflection in the signals collected by an array of antennas to
reconstruct and remove the skin reflection. Although these methods can significantly reduce
the skin contribution in the backscattered signal, they have some shortcomings. Both methods
use averaging to estimate the skin backscatter from the signals collected in different elements
of the antenna array. As a result, if the tumor is approximately equidistant to some of the
elements of the array, its reflection will suffer a high attenuation in the processed signals.
This will make the tumor detection very difficult or even impossible. Another problem of the
354
Novel Applications of the UWB Technologies
Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection 19
averaging based methods is that they add the averaged version of the noise and clutter from
all channels to each individual channel which makes the tumor detection even more difficult.
In addition, as the tumor reflection should not be included in the skin reflection estimation
process, these methods need to determine the early time part of the signal where only the skin

antenna-array sensors, IEEE Trans. Biomed. Eng. 45: 1470–1479.
Haykin, S. (1996). Adaptive Filter Theory, 3rd edn, Prentice-Hall.
J. Elwood and B. Cox and A. Richardson (1993). The effectiveness of breast cancer screening
by mammography in younger women, The Online journal of current clinical trials 32.
URL: />Keller, J. (1958). A geometrical theory of diffraction, Courant Institute of Mathematical Sciences,
New York University.
Kosmas, P. & Rappaport, C. (2005). Time reversal with the FDTD method for microwave
breast cancer detection, IEEE Transactions on microwave theory and techniques
53(7): 2317–2322.
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Frequency Domain Skin Artifact Removal Method for Ultra-Wideband Breast Cancer Detection
20 Will-be-set-by-IN-TECH
Li, X. & Hagness, S. (2001). A confocal microwave imaging algorithm for breast cancer
detection, IEEE Microwave and Wireless Components Letters 11(3): 130–132.
Moore, T., Zuerndorfer, B. & Burt, E. (1997). Enhanced imagery using
spectral-estimation-based techniques, Lincoln Laboratory Journal 10(2): 171–186.
Naishadham, K. & Piou, J. (2004). A super-resolution method for extraction of modal
responses in wideband data, IEEE Antennas and Propagation Society International
Symposium 4: 4168–4171.
Naishadham, K. & Piou, J. (2005). State-space spectral estimation of characteristic
electromagnetic responses in wideband data, IEEE Antennas and Wireless Propagation
Letters 4: 406–409.
Piou, J. (2005). A state identification method for 1-d measurements with gaps, Proc. American
Institute of Aeronautics and Astronautics Guidance Navigation and Control Conf. .
American Cancer Society (ACS) (2007). What are the key statistics for breast cancer?
URL: />_statistics_for_breast_cancer_5.asp
Center for Disease Control and Prevention (CDC) (2007). Statistics.
URL: />Ulger, H., Erdogan, N., Kumanlioglu, S. & Unur, E. (2003). Effect of age, breast size,
menopausal and hormonal status on mammographic skin thickness, Skin Research
and Technology 9: 284–289.

between the transmit (Tx) and receive (Rx) antennas, which determines the dynamic range
of the system, to be kept as small as possible [12].
In this book chapter, the full-wave analysis of electromagnetic coupling mechanisms
between resistively loaded wideband dipole antennas operating in realistic GPR scenarios is
carried out. To this end, a locally conformal finite-difference time-domain (FDTD)
technique, useful to model electromagnetic structures having complex geometry, is adopted
[1], [2]. Such a scheme, necessary to improve the numerical accuracy of the conventional
FDTD algorithm [19], [21], by avoiding staircase approximation, is based on the definition of
effective material parameters [14], suitable to describe the geometrical and electrical
characteristics of the structure under analysis. By doing so, the losses in the soil, as well as
the presence of ground-embedded inhomogeneities with arbitrary shape and electrical
properties, are properly taken into account. Emphasis is devoted to the investigation of the
antenna pair performance for different Tx–Rx separations and elevations over the ground,
as well as on scattering from dielectric and metallic pipes buried at different depths and
having different geometrical and electrical characteristics. Novelty of the analysis lies in the

Novel Applications of the UWB Technologies

360
fact that at the lowest operational frequency both the receive antenna and a pipe are situated
in the near-field, whilst at the highest operational frequency only the far field is playing the
role. The obtained numerical results provide a physical insight into the underlying
mechanisms of subsurface diffraction and antenna mutual coupling processes. This
information in turn can be usefully employed to optimize the performance of detection
algorithms in terms of clutter rejection.
Finally, a frequency-independent equivalent circuit model of antenna pairs is provided in
order to facilitate the design of the RF front-end of ground-penetrating radars by means of
suitable software CAD tools. The procedure employed to extract the equivalent circuit is
based on a heuristic modification of the Cauer’s network synthesis technique [10] useful to
model ohmic and radiation losses. In this way, one can obtain a meaningful description of

M
is composed of space-filling hexahedrons, whose vertices are defined by the Cartesian
coordinates:



(,,)| 0,, ; 0,, ; 0,, .
ijk x y z
xyz i N j N k N 
(1)
As a consequence, the edge lengths between adjacent vertices in
D
M
result to be expressed
as:

1
1
1
,0,1,,1,
,0,1,,1,
,0,1,,1.
ii i x
jj j y
kk k z
xx x i N
yy y j N
zz z k N



iii
xxx


 ,
1/2
/2
jjj
yyy


 ,
1/2
/2
kkk
zzz


 . A set of
dual edge lengths is then introduced in
D
M

as follows:





1




(3)
As usual, the electric field components are defined along each edge of a primary lattice cell,
whereas the magnetic field components are assumed to be located along the edges of the
secondary lattice cells. In this formulation, the relationship between
E

and
H 
field
components is given by Maxwell’s equations expressed in integral form, specifically using
Faraday-Neumann’s law and Ampere’s law, respectively. In particular, the enforcement of
the Ampere’s law on the generic dual-mesh cell surface
1/2, ,
x
i
j
k
S


having boundary
1/2, , 1/2, ,
xx
i
j
ki
j

Hrdl rr rr (4)
where:











11 11
22 22
1/2, ,
11 11
22 22
,,,,,,,
,, , ,, ,
k
x
ijk
j jk
zz k z k
ij ij
C
yy j y j y z
ik ik
tHxyztHxyzt

i
x ,
j
y ,
k
z of the computational grid are small compared to the minimum working wavelength,
the infinitesimal terms of higher order appearing in (5) can be neglected. Furthermore, it
should be noticed that the
x

component of the electric field is continuous along the
interfaces crossing
1/2, ,
x
i
j
k
S


so that, under the mentioned hypothesis, the following
approximation can be made:



1
2
1/2, , 1/2, ,
() (,) , , , () .
x x

() () () () ,
eff eff
xx xx
ijk ijk
ijk ijk
zzyy
ijk ijk
ijk ijk
tt
t
tttt


 
 






(7)
where we have introduced the normalized field quantities:



1
1
2
2

11
22
22
,,
() , , , ,
j
yyyj
ik
ijk
tHxyzt


  (10)
and the averaged effective permittivity
1/2, ,
eff
x
i
j
k
 , and conductivity
1/2, ,
eff
x
i
j
k
 , defined
as follows:



 

 


 

(11)
Full-Wave Modelling of Ground-Penetrating Radars:
Antenna Mutual Coupling Phenomena and Sub-Surface Scattering Processes

363

The time derivative in (7) is then evaluated using a central-difference approximation that is
second order-accurate if
E

and H

field components are staggered in time domain [19].
This results in the following explicit time-stepping relation:


1
2
11
1
11
22

22
2
22
11 11
1
11 11
22 22
2
22 22
,, ,,
,,
,, ,,
nn
n
nn
zzyy
x
ijk ijk
ijk
i
j
ki
j
k



 



E
x
eff
ijk
x
i
j
k
Q
Q






(14)

1
2
1
2
1
2
,,
()
,,
,,
,
1

,,
,,
,,
.
2
eff
x
ijk
eff
x
eff
ijk
x
i
j
k
t
Q







(16)
The update equations of the remaining components of the electric and magnetic field can be
easily derived by permuting the spatial indices i ,
j
, k and applying the duality principle

 and electrical conductivity 15mS m

 . The geometry of
the structure is depicted in Fig. 2. Fig. 2. Top and cross-sectional view of a resistively loaded dipole antenna pair located above
a lossy homogeneous half space. Structure characteristics:
40
d
lcm
,
5
d
Dmm
,
2.5mm
,
6
r

,
15mS m
. The reference system used to express the field quantities is
also shown.
The dipoles are denoted as dipole
#1
and dipole
#2
, respectively. In the considered

y
l





(17)
has been applied to the flairs of the considered radiators. In (17),
0

denotes the electrical
conductivity value at the input terminals of the antennas (
0y

), and 40
d
lcm

is the
length of each dipole, assumed to have diameter
5
d
Dmm

. In particular,
0
 has been
determined by means of a dedicated parametric analysis. In this way, the optimal value
0

max
1
f
GHz

of the
excitation voltage signal, which is the Gaussian voltage pulse described by the equation:

2
0
ˆ
() exp (),
GG
G
tT
vt V ut
T










(18)
where
ˆ



1
1
2
2
11
11
1
11 1 11 1
11 1 11 1
22
22
11 1
2
11
(,) (,)
,, ,,
,, ,,
,,
,
n
nn
n
EG EG
yy yy G
y
ij k ij k
ij k ij k
ij k

,,
,,
1
,
1
EG
y
ij k
EG
y
EG
ij k
y
ij k
Q
Q






(21)

1
11 1
2
1
11 1
2

with:

1
11 1
2
1
11 1
2
(,)
,,
,,
,
2
EG
y
eff
ij k
y
G
ij k
t
Q
R





(23)
1


1
2
11
11
1
22 2 22 2
22 2 22 2
22
22
22 2
2
11
(,) (,)
,, ,,
,, ,,
,,
,
n
nn
EL EL
yyyy
y
ij k ij k
ij k ij k
i
j
k



EL
ij k
y
ij k
Q
Q






(26)

1
22 2
2
1
22 2
2
1
22 2
2
,,
(,)
(,)
,,
,,
,
1

EL
y
eff
ij k
y
L
ij k
t
Q
R





(28)
Full-Wave Modelling of Ground-Penetrating Radars:
Antenna Mutual Coupling Phenomena and Sub-Surface Scattering Processes

36
7
and with
2
i ,
2
j ,
2
k denoting the spatial indices relevant to the load. The total voltage and
current signals excited at the input terminals of the antenna pair, regarded as a two-port
microwave network, are readily computed as:

ij k ij k i j k i j k
C
it t

   
   



Hr dl 
(30)
where
m
V
C is an open contour extending along the delta gap, and
m
I
C a closed contour path
wrapping around the driving point of dipole #m (
1,2m

). Under the mentioned
assumptions, the normalized incident and reflected waves are evaluated as:

1
110
0
()
1
() () ,

(32)

2
() 0,af (33)

2
2
0
()
() ,
Vf
bf
R
 (34)
where
0 G
RR
denotes the reference resistance and


() ()
mm
Vf vt F ,


() ()
mm
If it F ,
[]F


d
h decreases, the fundamental
resonant frequency of the dipole is shifted down because of the proximity effect of the soil.
On the other hand, the ground influence on the
21
S parameter is remarkable only at high
frequencies, where the coupling level between the two radiating elements tends to decrease
as the dipoles approach the air-ground interface.
In the performed numerical computations, a ten-cell uniaxial perfectly matched layer (UPML)
absorbing boundary condition for lossy media [19] has been used at the outer FDTD mesh
boundary to simulate the extension of the space lattice to infinity. As outlined in [19], the

Novel Applications of the UWB Technologies

368
UPML is indeed perfectly matched to the inhomogeneous medium formed by the upper air
region and the lossy material modelling the soil. So, no spurious numerical reflections take
place at the air-ground interface. In particular, a quartic polynomial grading of the UPML
conductivity profile has been selected in order to have a nominal reflection error
16
PML
Re

 . (a) (b)

interface and recording the output of the receive antenna as function of time (or frequency)
and radar location, one obtains the scattering data, which can be processed to get an image
of the subsurface. Fig. 5. Top and cross-sectional view of a resistively loaded dipole antenna pair located above
a lossy inhomogeneous ground, where an infinitely long pipe is buried. Structure
characteristics:
40
d
lcm , 5
d
Dmm , 2.5mm , 20
d
scm , 3
d
hcm , 30
p
Dcm

,
40
p
hcm .

Novel Applications of the UWB Technologies

370
The parasitic coupling level between transmit and receive antennas is a critical parameter in
the design of ground-penetrating radars and satisfactory levels are usually achieved by

4.1 Analysis of sub-surface scattering processes
The considered antenna pair has been used to analyze the sub-surface scattering
phenomena arising from the field interaction with a PVC pipe buried at a depth
30
p
hcm . As it can be easily inferred, the intensity of the radio signal diffracted by the
pipe and measured at the input terminals of the receive antenna strongly depends on the
electrical and geometrical properties of the target. In particular, the peak-to-peak level of
the signal increases as the diameter, and hence the radar cross section of the pipe becomes
larger (see Fig. 7). Another noticeable phenomenon is the sub-surface excitation of
creeping waves. Such waves, propagating along the pipe surface, give rise to late-time
pulse contributions in the received radio signal which can be clearly noticed in Fig. 7 as
the radius of the object increases. Furthermore, it is worth noting that the strength of the
creeping wave contribution tends to reduce with the pipe size because of the field
attenuation relevant to the extra-path length.
Full-Wave Modelling of Ground-Penetrating Radars:
Antenna Mutual Coupling Phenomena and Sub-Surface Scattering Processes

371Fig. 7. Time-domain behaviour of the radio signal diffracted by a PVC pipe buried at a
depth
30
p
hcm
in a lossy ground with electrical properties
6
r


2
,
1
,
2
r
r
e










(37)
with mean
13.7

 , and standard deviation 4.2


 (see Fig. 8). As it appears from Fig. 9,
the ground-embedded inhomogeneities have a considerable impact on the coupling
coefficient
21
S of the dipole pair especially at high frequencies ( 0.6