GEOMETRIC CHARACTERIZATION OF A TARGET

ABOVE THE HALF-SPACE INTERFACE

USING SUPPORT VECTOR MACHINE

Chao Li, Si-Yuan He ,Guo-Qing Yin and Guo-Qiang Zhu

School of Electronic Information, Wuhan University, Wuhan, China

Keywords: Support Vector Machine, Inverse Scattering, Composite Model, Multilevel UV Method.

Abstract: The geometric parameters of a electrically large square above a rough surface are reconstructed by means of

support vector machine (SVM). The SVM input data are the amplitude of backscattered electric fields

obtained from the accurate and efficient EM numerical simulation. The aim of our research is to reconstruct

the geometric information while using computational resources as reduced as possible. Therefore, how the

spatial and frequency diversity affect the reconstruction is analysed with respect to the characteristics of the

scattered fields. Numerical experiments show that it is feasible to get an accurate reconstruction result with

the backscattered multi-frequency data collected at just a few observation points which are specially

selected based on scattering characteristics.

1 INTRODUCTION

Both the scattering and the inverse scattering from a

target above the half-space interface have a broad

range of applications, such as target identification

and microwave remote sensing (Ye and Jin, 2006;

Deng et al., 2010).

The electromagnetic (EM) inverse scattering is to

recover some unknown information of the scattering

model through scattered fields probed at the

observation points where antennas are placed

(Bermani et al., 2002; Persico et al., 2005; Caorsi et

al., 2005; Qing, 2003). Compared with a target in the

free space, the inverse scattering from a target above

a rough surface is much more difficult because of

the complicated multiple-interactions between the

target and rough surface. In recent years, neural

networks (NN) and support vector machine (SVM)

are proposed to solve EM inverse problems. In

particular, as far as buried objects investigations are

concerned, NNs have been applied to face the

problem in the frequency/time domain (Bermani et

al., 2002; Pettinelli et al., 2009), while SVM is used

to deal with the buried objects detection (Caorsi et

al., 2005).

In the following, how the spatial and frequency

diversity affect the reconstruction is analyzed in

terms of electrically large objects by analyzing the

characteristics of the scattered field. In the end, the

side length and height of a two-dimensional

electrically large square above a rough surface are

successfully reconstructed from the backscattered

electric fields with the backscattered multifrequency

data collected at just a few observation points

(practically more convenient).

2 INVERSE PROBLEM

The geometry of the problem is shown in Figure 1, a

2-D PEC square with unknown side length

L is

located at a certain height of

above a PEC rough

surface, which is generated with the Pierson-

Moskowitz (P-M) spectrum. A truncation of the

rough surface is required and a tapered wave is

Figure 1: Geometry of the inverse problem.

352

Li C., He S., Yin G. and Zhu G..

GEOMETRIC CHARACTERIZATION OF A TARGET ABOVE THE HALF-SPACE INTERFACE USING SUPPORT VECTOR MACHINE .

DOI: 10.5220/0003722403520355

In Proceedings of the International Conference on Evolutionary Computation Theory and Applications (ECTA-2011), pages 352-355

ISBN: 978-989-8425-83-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

incident to avoid scattering effects from surface

edges (Ye and Jin, 2006). A TM polarized (with

electric field in

y direction) tapered wave

E is used

to illuminate the composite model with the incident

angle

. Suppose

is the distance between the

radar and the reference point

O .

The inverse problem considered is to reconstruct

the geometric parameters of the target, such as the

side length and the height, from the backscattered

electric fields. Mathematically, the problem reduces

to determine the following relation:

= （）EL (1)

where

is the scattered electric field array.

In the previous study, in order to get an

exhaustive information, many observation points are

set equally spaced on a measurement line to gather

the backscattered fields. In this paper, we consider

an efficient multifrequency–singleview-monostatic

det- ection way and the objects under study are

electric- ally large. How the spatial diversity and

frequency diversity affect the reconstruction is

analyzed.

3 NUMERICAL RESULTS

3.1 Traditional Case

In this section, we firstly reconstruct the side length

of a square above a rough surface using the

singlefrequency–multiview–monostatic configurati-

on, i.e., a measurement configuration wherein the

transmitter and the receiver are placed together at 21

equally spaced positions along the measurement line.

The incident wave is operating at 300MHz with the

freespace wavelength

1( )m

= . The training sampl-

es are

4.01 0.1 ( ), 0, 9Limi=+ ="

while the test

samples are

4.045 0.1 ( ), 0 8.Limi=+ ="

Wind spe-

U is 0/.msThe errors are quantified by the

following formula:

()| |/| |100

tr t

RelErr p p p p=− ×

Where

p is the considered unknown variable,

subscript

and r indicate the real value and the

reconstructed value of the variable respectively. The

average error is

2.0% .

Then, we use the multifrequency-singleview-

monostatic configuration. In this case, the incident

angle is

The training and test sets are the

same as we used above. The frequencies are chosen

according to the rule:

300 10 ( ), 0 9fiMHzi

+="

The average error is

0.6% .

3.2 The Frequency Diversity

In this section, we fix the observation point at which

the incident angle is

= The frequencies

100 10 ( ), 0...9fiMHzi=+ =

are chosen at first. Then

the frequencies

500 10 ( ), 0 9fiMHzi=+ ="

, which

belong to the resonance band according to the

electrical size and

1( ) 10 ( ), 0, 9f GHz i MHz i=+ ="

which belong to the optical band are chosen. The

wind speed is taken as

0/Ums

The average errors are shown in Table 1. When

the incident wave frequencies are raised up, the

average errors of the reconstruction get higher. This

unsatisfactory reconstruction results could be an

effect of the different scattering characteristics in

different frequency bands.

Table 1: Relative errors in the reconstruction.

Frequency

(MHz)

Average Maximum Minimum

100-190 0.1% 0.3% 0.05%

500-590 2.1% 3.9% 0.06%

1000-1090 4.4% 8.4% 0.8%

In order to investigate the scattering

characteristics in resonance and optical bands, we

fix the frequency

300

MHz

and

GHz

respectively and change

the square side length according to the rule:

4.01 0.1 ( ) 0, 39Limi

+=" . The results are shown

in Figure 2 and Figure 3.

Figure 2: The characteristic of scattered fields in optical

band.

Figure 3: The characteristic of scattered fields in optical

band.

GEOMETRIC CHARACTERIZATION OF A TARGET ABOVE THE HALF-SPACE INTERFACE USING SUPPORT

VECTOR MACHINE

353

As shown in the figures above, the scattered

electric fields in the optical band are characterized

by an acute oscillating profile while the one in the

resonance band is changing much more gently. In

order to overcome this problem, much more square

samples are needed. Figure 4 reports the amplitude

of electric fields for

GHz

with square side

lengths changing according to the rule:



4.01 0.03

(),

im i=+ ="

. The observation

point is still the one with incident angle

= .

In Figure 4, the accurate relationship between the

amplitude of the backscattered electric field and

square side length can be established and the profile

is oscillating much more gently. Actually, when the

number of square samples is increased, the

geometric information carried by the electric fields

are more completed and integrated which is

beneficial to the inverse scattering procedure.

Figure 4: The characteristic of scattered files in optical

band with more samples.

The analysis above gives us a hint on how to

improve the reconstruction results in optical band.

We redo the optical case with a new training

set:

4.01 0.015 ( ) , 0, 59Limi=+ ="

. The other compu-

tational parameters are kept the same. Now, the

reconstruction results are with an average error less

than

1% .

As can be argued from the above experiments, in

order to get an satisfactory reconstruction result,

more training samples are usually needed for the

optical band.

However, in these examples, the observation

point has been fixed at which the incident angle

In the section followed, we choose different

observation points to discuss how the spatial

diversity affects the reconstruction.

3.3 The Spatial Diversity

In this section, the role of the spatial diversity in the

reconstruction is investigated by means of changing

the observation points.

At first, The incident wave frequencies are

chosen according to the

rule

300 10 ( ), 0, 9.fiMHzi=+ ="

Then, three different

observation points with incident

angle

, and

respectively are

chosen to gather backscattered fields. The training

and test sets are the same as we used in 3.1. The

wind speed is taken as

0/Ums

The average errors with respect to the three

observation points are shown in Table 2. It is easy to

find that when the incident angle is

, we can

retrieve the square side lengths accurately. This

phenomenon may have relations to the dihedral

corner reflector consists of the square edge and the

bottom surface. We can fix the frequency

GHz=

and set the incident angle

investigate how the electric fields vary in terms of

the square side lengths. The square side lengths

selected are changing according to the rule:

4.01 0.1 ( ), 0, 39Limi=+ ="

. The results are showed in

Figure 5. It is interesting to find that the scattered

electric fields are changing much more gently and

linearly when the observation point is set at the one

with incident angle

. The special scattering

characteristics of the dihedral corner reflector are

beneficial to the inverse scattering procedure, which

implies the nonlinear regression is close to a linear

one.

Table 2: Relative errors in the reconstruction.

Incident

Angle

Average Maximum Minimum

22° 3.1% 6.9% 0.6%

45° 0.1% 0.3% 0.003%

70° 3.4% 6.2% 0.2%

Figure 5: The characteristic of scattered fields.

In section 3.2, when the incident angle is

we fail to retrieve the square side length in optical

band with the same training set used in resonance

band. The reconstructed results are improved by

increasing the number of training samples, which

obviously raises the burden of making training set.

What’s worse, the SVM needs more time to do the

regression. The above numerical simulation results

ECTA 2011 - International Conference on Evolutionary Computation Theory and Applications

354

tell us that when the incident angle is

= , it is

easier to get an satisfactory reconstruction results

due to the strong interaction of the dihedral corner

reflector. So, in the following , we will try to retrieve

the square side length when the training and test set

are kept the same as we used in resonance band as

4.01 0.1 ( ), 0, 9Limi=+ ="

and

4.045 0.1 ( ), 0 8Limi=+ ="

respectively. However, the observation point with

will be used instead of the one with

The wind speed is taken as

0/Ums=

The reconstruction results with an average error

less than

1% which means the square side lengths

are accurately reconstructed for optical band with

the same training set as we used in resonance band.

3.4 Reconstruction in Multifrequency–

Singleview-Monostatic Way

In this section, the bottom surface is a rough surface.

Because of the roughness of the bottom surface,

more observation points are often needed to capture

the special scattering characteristics of the dihedral

corner reflector consists of the square edge and the

bottom surface. In addition to the side length, the

height of the square above the surface is retriev- ed.

The values of

L considered during the training

phase are

4.01 0.05 ( ), 0...19Limi=+ =

, while the

height

7.01+0.01 ( ), 0...9Himi==

The test set is obtained by setting the square

side length as

4.045 0.1 ( ), 0 8Limi=+ ="

, and the

height are set as

7.015 0.01 ( ), 0...8Himi=+ =

. The

incident wave frequencies are chosen as:

200 10 ( ), 0...9fiMHzi=+ =

. The wind speed is

3/Ums= .

The relative errors with observation points set at

and

are shown in Table 3. Both the

side length and height are retrieved accurately. The

relative errors reconstructed with 21 observation

points set equally along the measurement line are

shown in Table 4 for a comparison.

From Table 3 and Table 4, it is interesting to find

that the errors are almost the same and sometimes

the one reconstructed with more observation points

Table 3: Relative errors of side length and height for 3

observation points.

Average Maximum Minimum

RelErr(H) 0.05% 0.17% 0.0003%

RelErr(L) 0.11% 0.33% 0.001%

Table 4: Relative errors of side length and height for 21

observation points.

Average Maximum Minimum

RelErr(H) 0.06% 0.17% 0.0001%

RelErr(L) 0.12% 0.39% 0.001%

has slightly higher errors. That is to say, more

observation points do not guarantee a better

reconstruction results. As a second remark, more

observation points consume much more computatio-

nal resources.

4 CONCLUSIONS

In this paper, we investigated the geometric

parameters reconstruction of an electrically large

square above the rough surface. The role of the

spatial and frequency diversity in the reconstruction

is investigated in detail with respect to the

characteristics of the scattered field. At last, the side

length and height of the square above the rough

surface are retrieved accurately with the

backscattered multifrequency data collected at just a

few observation points which are specially selected

based on the scattering characterisitics.

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