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Comparison of Basic Inversion Techniques for

Through-Wall Imaging Using UWB Radar

N.T. Th` anh1, L. van Kempen1, T.G. Savelyev2, X. Zhuge2, M. Aftanas3, E. Zaikov4, M. Drutarovsk´ y3, H. Sahli1

1Dept. of Electronics & Informatics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium

{ntthanh, lmkempen, hsahli}@etro.vub.ac.be

2International Research Centre for Telecommunications and Radar, Delft University of Technology

Mekelweg 4, 2628 CD Delft, the Netherlands

T.G.Savelyev@irctr.tudelft.nl, X.Zhuge@ewi.tudelft.nl

3Dept. of Electronic and Multimedia Communications, Technical University of Koˇ sice

Park Komensk´ eho 13, 04120 Koˇ sice, Slovak Republic

{Michal.Aftanas, Milos.Drutarovsky}@tuke.sk

4Dept. of Electronic Measurement Research Lab, Technical University of Ilmenau,

POB 100565, D-98684 Ilmenau, Germany

Yahor.Zaikou@tu-ilmenau.de

Abstract—In this paper, we consider the problem of de-

tecting and localizing static objects in a room using though-

wall Ultra-WideBand (UWB) radar SAR measurements. This

paper investigates basic inversion (imaging) techniques which are

used for interpreting the raw radar data in an understandable

way. We also introduce a fast method for estimating the travel

time between the antennas and the targets. The accuracy and

computational complexity of the imaging techniques are analyzed

and compared.

I. INTRODUCTION

Through-wall imaging using radar offers a powerful tool

for safety and security applications such as rescue operations,

surveillance and hostage situations. In raw radar data, the

information of targets is usually shown as hyperbolae. The

aim of imaging techniques is to reconstruct the location and

shape of the targets by focusing the hyperbolae to their true

locations. Imaging methods can be divided into two categories:

back-projection methods (they are also referred to as ray-

based methods) and back-propagationmethods (or wave-based

methods). Back-projection methods make use of the direct ray

path between the antennas and the targets and thus the electro-

magnetic wave theory is not taken into account. In contrast,

back-propagation methods are based on the electromagnetic

wave theory and can be subdivided into time-domain and

frequency-domain methods. We note that this classification

was not consistent in the literature.

The key point of these imaging methods is the estimation

of the travel time between antennas and a possible target. A

factor that must be taken into account when applying these

imaging methods to through-wall data is the time delay due

to propagation of the wave inside the wall. Ignoring this time

delay can not only displace the reconstructed targets from

their true positions but also defocus the target images. In this

paper, we evaluate the performance of three basic imaging

techniques: Synthetic Aperture Radar (SAR) (or diffraction

stack migration), Kirchhoff migration and Stolt migration

(or f-k migration). Moreover, we propose a fast method for

calculating the travel time in through-wall scenarios.

In order to evaluate the imaging methods and compare their

results, we introduce two parameters: the Signal to Clutter

Ratio (SCR), which is defined as the ratio of the energy

between the estimated regions of the objects and the clutter

regions, and the relative positioning error (RPE), which is

defined as the ratio between the error in the object position

estimation and the ground truth. A good reconstruction method

should have a large SCR and a small RPE.

The paper is organized as follows. Section II describes the

measurement scenario used in this paper, system specification

and data pre-processing steps. In Section III, the basic imaging

techniques are briefly described. The estimation of the travel

time is presented in Section IV. Section V is devoted to

reconstruction results and analysis. Finally, some conclusions

are drawn in Section VI.

II. MEASUREMENT SETUP AND DATA PRE-PROCESSING

A. Measurement Setup and System Specification

A simplified sketch of the measurement layout is shown in

Fig. 1. The radar system was horizontally scanned parallel to

the front brick wall (with a thickness of 18 cm) at a distance of

50 cm from the wall between position 1 and position 2. In this

paper, we illustrate the performance of the imaging algorithms

for the data of an aquarium of size 50 × 30 × 30 (cm) filled

with water (Fig. 2(b)). The object was placed inside the room

at position 3 which is at the center of the scanning range and

1 m far from the inside of the wall.

The UWB system used in this experiment is a pseudo

random noise radar which consists of one transmitter and

two receivers. The frequency band is between 800 MHz and

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4.5 GHz. The antennas were fixed on a trolley in a vertical

mask with the transmitter in the middle (see Fig. 2(a)). The

distance between the center of the transmitting antenna and

each of the receivers is 45 cm.

Position 1

Position 2

Antennas

2 m

Position 3

Wooden

Door

Aquarium

0.18 m

0.5 m

0.35 m

1.05 m

1 m

4.08 m

4.57 m

Rear Wall

Front Wall

Fig. 1. The through-wall SAR measurement scenario.

(a) (b)

Fig. 2.

aquarium filled with water.

The through-wall measurement scenario: (a) Radar system; (b) An

B. Data Pre-processing

Before applying the imaging techniques, some pre-

processing steps (time zero compensation, data interpolation,

low-pass filtering, crosstalk removal and deconvolution) were

applied to the measured raw data. The purpose of time zero

compensation is to find, in the measured radar data, the exact

time instant at which a signal is emitted from the transmitter

and accordingly shift the measured data. Data interpolation

is used to up-sample the measured data in both time and

space variables. Low-pass filtering is applied to suppress

any quantization noise. Deconvolution sharpens the received

impulses by compensating for the radar transfer function. For

more details on data pre-processing, the reader is referred to

[6], [8], [10].

III. FORMULATION OF BASIC IMAGING TECHNIQUES

In this section, we summarize the formulation of three basic

imaging techniques: SAR, Kirchhoff and Stolt migrations.

Since the vertical resolution of the measured data is very low,

we only consider a B-scan and focus it on the bisecting (hor-

izontal) plane of a transmitter-receiver pair. On this plane, we

define a Cartesian coordinate system of which the coordinates

of a point are denoted by (x,z), where x is in the scanning

(cross-range) direction and z represents the coordinate in the

range direction. We denote by ϕ(x,t) a measured B-scan with

t being the time variable. A focused image in the object space

is denoted by I(x,z).

A. Synthetic Aperture Radar

SAR is a back-projection imaging method that was first

developed for airborne radar applications, and later adapted

to Ground Penetrating Radar (GPR) [4], [8]. The algorithm

is based on the fact that an object contributes to the received

waveforms with different time delays which depend on the

distance between the antennas and the object. The object

distribution can be estimated by focusing the received data

using the following formula

?

where Δtxais the travel time from the transmitter to the point

P(x,z) and back to the receiver. The integration is taken along

the scanning path. Note that the travel time in free space is

given by

I(x,z) =

ϕ(xa,Δtxa)dxa,

(1)

Δtxa= [d(Txa,P) + d(Rxa,P)]/c,

with d(Txa,P) and d(Rxa,P) being the distances from the

transmitter Txato the point P and from P to the receiver

Rxa, respectively; c the light speed in free space.

The computational complexity of the SAR algorithm is of

O(NxNzNa), where Nx and Nz are the number of points

in the x- and z-directions in the object space at which the

reconstruction is done, Na is the number of A-scans. By

subdividing the synthetic aperture into smaller ones, Yegu-

lalp [9] showed that we can speed up by a factor of

Nx= Nz= Na= N.

√N if

B. Kirchhoff Migration

Kirchhoff migration is based on the Kirchhoff integral

theorem representing the solution of the wave equation using

Green’s functions [3], [5]. Using the closed form of the

Green’s function for homogeneous media, the migrated field at

a point P(x,z) in a 2D homogeneous space for a monostatic

radar system can be approximated by the following formula

[3]

?

where θ is the angle between the z axis and the line joining

the point P(x,z) and the position of the antenna Txa; ∂1/2

represents the half derivative with respect to time variable t.

It is defined via frequency domain as

I(x,z) =

cosθ

√πrv∂1/2

t

ϕ(xa,Δtxa)dxa,

(2)

t

F∂1/2

t

ϕ(ω) = (iω)1/2Fϕ(ω).

Here F is the Fourier transform. r is the distance from the

antenna to the point P and v is the wave propagation speed.

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Note that (2) is formulated for homogeneous media. How-

ever, in this paper, it is also used in through-wall scenarios

with an adaptation for the travel time Δtxa(Section IV).

Concerning the computational cost, the Kirchhoff migration

is a bit more expensive than SAR as we need to calculate the

derivative with respect to the time variable of the received

signals. However, they are still in the same order as the cost

for numerical integration dominates that of the fast Fourier

transform used for calculating the derivative.

C. Stolt Migration

The F-k migration (also referred to as Stolt’s migration) is

a Fourier transform-based method developed from an exact

solution to the wave equation. It is a solution to the migration

problem for constant velocity in the propagation medium. It is

a direct method that is the fastest known migration technique.

The use of F-k migration was first proposed by Stolt [7]

for efficient processing of seismic data. This approach was

later used also for GPR and UWB signal processing [2]. He

formulated a migration solution that allows using the 2D FFT

for computationally efficient processing. The basic formula of

F-k migration is given by

??

where f = v?k2

φ0(kx,f) =

ϕ(xa,t)e−2πi(kxxa−ft)dxadt.

I(x,z) =

vkz

x+ k2

?k2

x+ k2

z

φ0(kx,f(kz))e2πi(kxx−kzz)dkxdkz,

(3)

zand

??

The computational complexity of the F-k migration is of

O(NxNzlog2Na) which is known as the fastest available

migration algorithm. However, certain distortion can appear

as it requires the interpolation from (kx,f) to (kx,kz). Hence

there is a tradeoff between distortion and complexity.

IV. TRAVEL TIME ESTIMATION

In through-wall scenarios, the time that a signal travels

between the antennas and possible objects cannot be directly

calculated unlike in homogeneous media. Instead, we have to

take into account the refraction of the signal at the interface

between layers. In general, the calculation of the travel time

in multi-layered media is very time consuming. In this paper,

we use a fast method for approximating it as in the case of

2-layered media. The idea was partly presented in [1].

For a 2-layered medium as shown in Fig. 3(a), the signal

from the antenna A to the point P follows the path ABP.

The inflection point B can be approximated as [4]

??1

By simple manipulations, we can represent the inflection point

B in terms of the positions of the antenna A, the point P and

their projections on the interface as follows

??1

− − →

BP1=

?2

− − →

CP1.

− − →

BP1=

?2

|PP1|− − − →

|AA1| + |PP1|.

A1P1

(4)

(a) (b)

Fig. 3.Signal travel path in (a) 2-layered and (b) 3-layered media.

To calculate the travel path from antenna A to P in the

through-wall scenario shown in Fig. 3(b), we imagine that the

wall is ”moved” toward the point P. From the figure we can

see that the travel time following the path AB1B2P is the

same as that of the path AB3P. So it is enough to calculate

the coordinates of B3. Using (4) we arrive at

??1

The travel time is then easily calculated from (5). It is used

in SAR and Kirchhoff migration. However, in Stolt migration

this method was not used. Instead, a constant time shift was

considered in order to compensate for the time delay inside

the wall.

− − − →

B3P2=

?2

|PP2|− − − →

|AA2| + |PP2|.

A2P2

(5)

V. RECONSTRUCTION RESULTS AND ANALYSIS

In this section, we show and compare the reconstruction

results of the imaging algorithms described in Section III for

the aquarium. The absolute values of the focused images using

SAR, Kirchhoff migration and Stolt migration are depicted in

Fig. 4, 5 and 6, respectively. Fig. 7 shows some range-profiles

of the focused SAR image.

From the figures we can see that the aquarium as well as

the rear wall are visible in all migrated images. However,

they are most clearly visible in the SAR result. SAR and

Kirchhoff migration give almost the same location for the

front wall (at approximately 58 cm far from the radar) and

the aquarium (at approximately 1.78 m) while these estimated

by Stolt migration are respectively 56 cm and 1.82 m. The rear

wall is estimated at about 4.8 m far from the radar systems

in all methods. Note that there is a shift of about 6–8 cm in

the location of the front wall compared to the ground truth

measured from the front size of the antennas to the wall.

TABLE I

RESULTS OF THE CONSIDERED IMAGING METHODS.

Method

SAR

Kirchhoff migration

Stolt migration

Comp. complexity

O(NxNzNa)

O(NxNzNa)

O(NxNzlog2Na)

SCR

2.57

1.64

1.51

RPE

1.136%

1.136%

3.409%

The SCR and RTE of these methods for the aquarium are

given in Table I. Note that the values of the SCR depend on

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Cross−range (scanning direction) (m)

Range (looking direction) (m)

0 0.51 1.52

0.2

0.7

1.2

1.7

2.2

2.7

3.2

3.7

4.2

4.7

5.2

aquarium

rear wall

front wall

Fig. 4. Focused image using SAR.

Cross−range (scanning direction) (m)

Range (looking direction) (m)

0 0.51 1.52

0.2

0.7

1.2

1.7

2.2

2.7

3.2

3.7

4.2

4.7

5.2

front wall

aquarium

rear wall

Fig. 5. Focused image using Kirchhoff migration.

the region in which it is calculated. However, we can conclude

that SAR and Kirchhoff migration are of the same accuracy

which is higher than that of Stolt migration. Besides, SAR

gives the strongest object signal while Stolt migration gave

the weakest one.

Concerning the computational complexity, Stolt migration

is the fastest method, even compared with the fast SAR algo-

rithm [9]. Indeed, if Nx= Nz= Na= N, their computational

complexity are respectively N2log2N and N5/2.

VI. CONCLUSIONS

We have investigated the performance of three basic imag-

ing methods (SAR, Kirchhoff migration and Stolt migration)

in through-wall scenarios. The results showed that for the

considered data, SAR is the best one in terms of accuracy

and quality of the focused image. However, Stolt migration is

the fastest method among them.

ACKNOWLEDGMENT

This work was supported by the EC project RADIOTECT,

within the European Community’s Sixth Framework Pro-

gramme, under the contract number COOP-CT-2006-032744.

Cross−range (scanning direction) (m)

Range (looking direction) (m)

0 0.51 1.52

0.2

0.7

1.2

1.7

2.2

2.7

3.2

3.7

4.2

4.7

5.2

front wall

aquarium

rear wall

Fig. 6. Focused image using Stolt migration.

1

Range (looking) direction (m)

2345

−2

−1

0

1

2

3

4x 10

−3

Received signal

At 0.4 m in cross−range

At 1.2 m in cross−range

Fig. 7.Focused signals in the range direction using SAR.

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