# CLEAN Technique for Polarimetric ISAR

Authors: M. Martorella; A. Cacciamano; E. Giusti; F. Berizzi; B. Haywood; B. Bates
Journal: International Journal of Navigation and Observation
 (2008)

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## Abstract

Inverse synthetic aperture radar (ISAR) images are
often used for classifying and recognising targets. To reduce the
amount of data processed by the classifier, scattering centres
are extracted from the ISAR image and used for classifying
and recognising targets. This paper addresses the problem
of estimating the position and the scattering vector of target
scattering centres from polarimetric ISAR images. The proposed
technique is obtained by extending the CLEAN technique, which
was introduced in radar imaging for extracting scattering centres
from single-polarisation ISAR images. The effectiveness of the
proposed algorithm, namely, the Polarimetric CLEAN (Pol-CLEAN) is tested on simulated and real data.


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## Body

## 1. Introduction

The CLEAN algorithm was introduced in radio astronomy
to reduce sidelobe-induced artefacts. In [1], the authors use the CLEAN technique to alleviate two
types of artefacts introduced by the point spread function (PSF) sidelobes in
real aperture radar images. Such a technique iteratively estimates the PSF of
the brightest scatterer and removes it from the formed image. The CLEAN technique was applied later to inverse
synthetic aperture radar (ISAR) imaging with interesting results [2]. Recently, fully
polarimetric radars have been largely used for synthetic aperture radar (SAR)
application [3, 4] as well as, although less extensively, for ISAR
applications [5]. The advantage
of fully polarimetric data is due to the fact that scattering mechanisms and
target properties can be identified by measuring scattering matrices [6–9]. Inverse synthetic aperture
radar (ISAR) images prove useful when used for classifying and recognising
targets [10, 11]. Nevertheless, the image
data size is often too large to implement real time classifiers. For this
reason, algorithms such as the CLEAN technique can be employed for reducing the
data size significantly without losing useful information. The problem of
reducing the amount of data without losing useful information is even more
critical when dealing with polarimetric ISAR images, since the data size is
three to four times larger. An algorithm for scattering centre extraction from
polarimetric SAR (PolSAR) images was proposed in [12]. In [12], the signal model was strongly
based on the SAR geometry, which is known a priori. In the ISAR case, the
non-cooperativity of the target does not allow using any such knowledge. So a
parametric model is introduced to account for unknown target motions.
Therefore, the problem of estimating the model parameters and the scattering
centre extraction problem must be solved jointly. Moreover, in typical ISAR
scenarios, only the received radar echo is presumed to be available (no
ancillary data is used). In this paper, a polarimetric CLEAN (Pol-CLEAN)
technique is proposed by extending the CLEAN technique in [2] in order to extract target
features such as the position of the scattering centres and their scattering
matrix. It is worth pointing out that the novelty of the proposed Pol-CLEAN
technique, with respect to the CLEAN technique, lies on the extension to
polarimetric ISAR images and on a new method for estimating the scattering
centre point spread function.The signal model is introduced in Section2 whereas
the Pol-CLEAN technique is detailed in Section 3. The effectiveness of the
proposed algorithm is tested on simulated and real data and presented in
Section 4.


## 2. Signal Model

The polarimetric matrix of the received signal, in
free space conditions, can be written in a time-frequency domain by extending
the signal model defined in [13](1)SR(f,t)=W(f,t)exp[−j4πfcR0(t)]⋅∫Vζ(z)exp{−j4πfc[zT⋅iR0(z)(t)]}dz+N(f,t), where SR(f,t)=[SRHH(f,t)SRHV(f,t)SRVH(f,t)SRVV(f,t)] is expressed by means of a polarimetric
matrix,
W(f,t)=rect[t/Tobs]rect[(f−f0)/B] represents a rectangular window in the
time-frequency domain (t,f),f0 is the carrier frequency, B is the
transmitted signal bandwidth, Tobs is the observation time, V is the
spatial domain where the scattering matrix ζ(z)=[ζHH(z)ζHV(z)ζVH(z)ζVV(z)] is defined, and N(f,t)=[NHH(f,t)NHV(f,t)NVH(f,t)NVV(f,t)] is the polarimetric matrix containing the
noise. With reference to Figure 1, z is the vector that locates a
generic scatterer, R0(t) is the modulus of vector R0(t),
which locates the focusing point O and iR0(z)(t) the unit vector of R0(t). The function rect(x) is equal
to 1 for |x|<0.5,0 otherwise.Figure 1
Radar-target geometry.Before proceeding, it is convenient to use a different
notation, as detailed in [7], and exploit the characteristic of isotropic media
that are encountered in ISAR applications. Therefore, the polarimetric data
that represents the received signal can be written according to
Pauli's decomposition as follows: (2)SR=12[SRVV+SRHH,SRVV−SRHH,2SRHV]T=Ak, where A=|k| and where the dependence on (f,t) is omitted for notation simplicity. The polarimetric unit vector k is defined as follows: (3)k=[cosαejδ,sinαcosβejγ,sinαsinβejφ], where β represents the physical rotation of the
scatterer about the radar line of sight (LoS), δ,γ,
and φ are the scatterer phases in the three
polarimetric channels, and α is a scatterer internal degree of freedom,
which ranges in the interval [0°,90°] . It must be pointed out that the angle α is rotation invariant and therefore it is
decoupled from β.
An interpretation of the internal degree of freedom α is given in Figure 2.Figure 2
Interpretation of the internal degree of freedomα.It is worth noting that such a representation is meant
to highlight the physical properties of the scattering mechanism induced by a
given scatterer. Therefore, by defining the unit vectork,
it is possible to define a specific polarisation that resonates with a
scatterer with given physical properties. It must also be pointed out that the
same decomposition applies for the target scattering matrix. Therefore, the
scattering vector obtained from the scattering matrix is ζ(z)=[ζVV(z)+ζHH(z),ζVV(z)−ζHH(z),2ζHV(z)].


### 2.1. Signal Separation

The Range-Doppler technique is based on an
approximation that allows considering a rectangular support for the received
signal in the Fourier domain. Such an approximation also leads to the
separation of the domain in two independent one-dimensional domains: a time and
a frequency component. Therefore, the received signal, relative to a single
point-like scatterer, can be written in terms of the product of a time and a
frequency component as follows:(4)sR(i)(t,f)=s1(i)(t)s2(i)(f), where (5)s1(i)(t)=Biexp(j2π(η+fdt+μ2t2))rect(tTob),(6)s2(i)(f)=Aiexp(j2πfτ0)rect(f−foB), where the product AiBi represents the complex amplitude in the ith
Pauli channel, fd is the Doppler frequency, μ is the chirp rate, and τ0 is the time delay associated with the
scattering centre. It is worth pointing out that the parameter μ is related to the signal model, which accounts
for a quadratic radial motion, that is, it includes Doppler acceleration.
Therefore, it should not be confused with the transmitted signal chirp rate if
any is employed.


## 2.1. Signal Separation

The Range-Doppler technique is based on an
approximation that allows considering a rectangular support for the received
signal in the Fourier domain. Such an approximation also leads to the
separation of the domain in two independent one-dimensional domains: a time and
a frequency component. Therefore, the received signal, relative to a single
point-like scatterer, can be written in terms of the product of a time and a
frequency component as follows:(4)sR(i)(t,f)=s1(i)(t)s2(i)(f), where (5)s1(i)(t)=Biexp(j2π(η+fdt+μ2t2))rect(tTob),(6)s2(i)(f)=Aiexp(j2πfτ0)rect(f−foB), where the product AiBi represents the complex amplitude in the ith
Pauli channel, fd is the Doppler frequency, μ is the chirp rate, and τ0 is the time delay associated with the
scattering centre. It is worth pointing out that the parameter μ is related to the signal model, which accounts
for a quadratic radial motion, that is, it includes Doppler acceleration.
Therefore, it should not be confused with the transmitted signal chirp rate if
any is employed.


## 3. Pol-CLEAN

The Pol-CLEAN technique is derived from the CLEAN
technique proposed in [2]. Specifically, the Pol-CLEAN works iteratively by(1)
locating the brightest scattering centre in
the polarimetric ISAR image and therefore by finding its coordinates in the
delay-Doppler image plane(τ*,ν*),(2)
extracting its polarimetric vectorks,
and(3)
removing it from the ISAR image in order to
extract the next brightest scattering centre. In order to
eliminate a scattering centre from an ISAR image, the scattering centre point
spread function (PSF) must be estimated and subtracted from the ISAR image. Let S(1)(f,t),S(2)(f,t) and S(3)(f,t) be the received signal in the three Pauli
channels. After motion compensation, three ISAR images, namely, I(1)(τ,ν),I(2)(τ,ν) and I(3)(τ,ν) are obtained by means of a 2D Fourier
Transform. The brightest scattering centre (dominant scatterer) is found within
the three images. The range and cross-range indexes τ* and ν* and the Pauli's channel i*,
which corresponds to the polarimetric channel that contains the brightest
scattering centre, are extracted by means of (7) (7)(τ*,ν*,i*)=argmax(τ,ν,i){|I(i)(τ,ν)|}, with i∈{1,2,3},τ∈{1,2,…,M},ν∈{1,2,…,N} and where M and N are the number of range and cross-range bins.
The estimation of the PSF is performed by minimising the image energy after
scattering centre removal. In order to find an efficient solution of the nonlinear
optimisation problem stated in (7), the received signal separation is
exploited.


### 3.1. Time Component

By referring to (5), Bi(i∈{1,2,3}),fd, and μ are the parameters to be estimated. The
constant η can be neglected, because it does not affect
the shape of the PSF. The signal s1(i)(t),
which is an N-dimensional row vector, is Fourier
transformed to obtain a cross-range profile. A cost function is defined by
means of the energy remaining in the range bin after scattering centre
deletion. In order to treat the optimisation problem in a real domain, the
scattering centre deletion is performed by considering the absolute value of
the range profile. Such an operation can be performed in a single channel and
then applied to the remaining channels by adjusting the corresponding Bi parameter. It must be pointed out that only
the magnitude B˜ of B must be estimated at this stage whereas the
phase component is estimated separately and directly from the image. In summary, the following optimisation problem can be stated: (8){f^d,μ^,B˜^i*}=argmin(fd,μ,B˜i*){Edi*(fd,μ,B˜i*)}, where Edi*=∫|di*(ν)|2dν is the energy of a Doppler section in the i*th Pauli channel, with di*(ν)=|I(i*)(τ*,ν)|−|S1(i*)(ν)| and S1(i*)(ν) the Fourier Transform of s1(i*)(t).
The estimates f^d and μ^ are then used in the remaining Pauli channels
for estimating the complex amplitudes Bi (with i≠i*). The latter estimation problem is
transformed into an optimisation problem as follows: (9){B˜^i}=argminB˜i{Edi(f^d,μ^,B˜i)withi≠i*}, where Edi=∫|di(ν)|2dν is the energy of a Doppler section in the ith Pauli channel (i≠i*) with di(ν)=|I(i)(τ*,ν)|−|S1(i)(ν)|.


### 3.2. Frequency Component

A similar procedure is followed to estimate the
frequency component of the PSF. The signal component in (6) is an M-dimensional
column vector. After selecting a Doppler bin and range compressing via the
Fourier Transform, a section of the ith channel ISAR image I(i)(τ,ν*) can be obtained. Then, the delay τ0 is jointly estimated with the magnitude A˜i* (in the i*th Pauli channel) as follows: (10){τ^0,A˜^i*}=argmin(τ0,A˜i*){Egi*(τ0,A˜i*)}, where Egi*=∫|dgi*(ν)|2dν is the energy of a delay section in the i*th Pauli channel, with gi*(ν)=|I(i*)(τ,ν*)|−|S2(i*)(τ)| and S2(i*)(τ) the inverse fourier transform of s2(i*)(f).The remaining two complex amplitudes are separately
estimated by solving two separate one-dimensional optimisation
problems:(11)A˜i=argminA˜i{Egi(τ^0,A˜i)}withi≠i*, where Egi=∫|dgi(ν)|2dν is the energy of a delay section in the ith
Pauli channel (i≠i*) with gi(ν)=|I(i)(τ,ν*)|−|S2(i)(τ)|.


### 3.3. Scattering Centre PSF

The scattering centre PSF in theith Pauli
channel is obtained by calculating the two dimensional Fourier Transform of the
product of the time and frequency components multiplied by the phase extracted
from the ISAR image, as analytically detailed in (12)IPSF(i)(τ,ν)=|FT2{s^1(i)(t)s^2(i)(f)}|⋅∠(I(i)(τ,ν)). The scattering vector ks(τ*,ν*) relative to the considered scattering centre
is therefore available by calculating the three scattering centre PSF centred
in (τ*,ν*).
Then, at the generic kth iteration, the scattering centre must be
eliminated from the ISAR image via (13) in order to extract the following
brightest scatterer: (13)Ik+1(i)(τ,ν)=Ik(i)(τ,ν)−IPSFk(i)(τ,ν). The algorithm stops when the
energy of the signal component in the ISAR image at the kth iteration is
lower than a given threshold, λ.
Such a threshold is typically set to 5% of the initial energy, that is, the
total energy of the polarimetric ISAR image before any component removal. In
mathematical detail, the preset threshold depends on the energy content and on
the SNR of the initial ISAR image, as detailed in (14) (14)λ=K⋅ESNRSNR+1, where E(I(τ,ν))=∑i=13E(I(i)(τ,ν)), with E(I(i)(τ,ν))=∬|I(i)(τ,ν)|2dτdν.
It is worth pointing out that a coefficient SNR/(SNR+1) is used in order to account for the energy of
the signal component (noiseless image). Moreover, the SNR can be estimated in
the image domain by selecting image areas where no target is present. It must
also be noted that the energy of the signal component of the ISAR image at each
iteration has to be compared to the energy threshold in (14). Therefore, the
iterations stop when Ek(I(τ,ν))(SNR/(SNR+1))<λ.


## 3.1. Time Component

By referring to (5), Bi(i∈{1,2,3}),fd, and μ are the parameters to be estimated. The
constant η can be neglected, because it does not affect
the shape of the PSF. The signal s1(i)(t),
which is an N-dimensional row vector, is Fourier
transformed to obtain a cross-range profile. A cost function is defined by
means of the energy remaining in the range bin after scattering centre
deletion. In order to treat the optimisation problem in a real domain, the
scattering centre deletion is performed by considering the absolute value of
the range profile. Such an operation can be performed in a single channel and
then applied to the remaining channels by adjusting the corresponding Bi parameter. It must be pointed out that only
the magnitude B˜ of B must be estimated at this stage whereas the
phase component is estimated separately and directly from the image. In summary, the following optimisation problem can be stated: (8){f^d,μ^,B˜^i*}=argmin(fd,μ,B˜i*){Edi*(fd,μ,B˜i*)}, where Edi*=∫|di*(ν)|2dν is the energy of a Doppler section in the i*th Pauli channel, with di*(ν)=|I(i*)(τ*,ν)|−|S1(i*)(ν)| and S1(i*)(ν) the Fourier Transform of s1(i*)(t).
The estimates f^d and μ^ are then used in the remaining Pauli channels
for estimating the complex amplitudes Bi (with i≠i*). The latter estimation problem is
transformed into an optimisation problem as follows: (9){B˜^i}=argminB˜i{Edi(f^d,μ^,B˜i)withi≠i*}, where Edi=∫|di(ν)|2dν is the energy of a Doppler section in the ith Pauli channel (i≠i*) with di(ν)=|I(i)(τ*,ν)|−|S1(i)(ν)|.


## 3.2. Frequency Component

A similar procedure is followed to estimate the
frequency component of the PSF. The signal component in (6) is an M-dimensional
column vector. After selecting a Doppler bin and range compressing via the
Fourier Transform, a section of the ith channel ISAR image I(i)(τ,ν*) can be obtained. Then, the delay τ0 is jointly estimated with the magnitude A˜i* (in the i*th Pauli channel) as follows: (10){τ^0,A˜^i*}=argmin(τ0,A˜i*){Egi*(τ0,A˜i*)}, where Egi*=∫|dgi*(ν)|2dν is the energy of a delay section in the i*th Pauli channel, with gi*(ν)=|I(i*)(τ,ν*)|−|S2(i*)(τ)| and S2(i*)(τ) the inverse fourier transform of s2(i*)(f).The remaining two complex amplitudes are separately
estimated by solving two separate one-dimensional optimisation
problems:(11)A˜i=argminA˜i{Egi(τ^0,A˜i)}withi≠i*, where Egi=∫|dgi(ν)|2dν is the energy of a delay section in the ith
Pauli channel (i≠i*) with gi(ν)=|I(i)(τ,ν*)|−|S2(i)(τ)|.


## 3.3. Scattering Centre PSF

The scattering centre PSF in theith Pauli
channel is obtained by calculating the two dimensional Fourier Transform of the
product of the time and frequency components multiplied by the phase extracted
from the ISAR image, as analytically detailed in (12)IPSF(i)(τ,ν)=|FT2{s^1(i)(t)s^2(i)(f)}|⋅∠(I(i)(τ,ν)). The scattering vector ks(τ*,ν*) relative to the considered scattering centre
is therefore available by calculating the three scattering centre PSF centred
in (τ*,ν*).
Then, at the generic kth iteration, the scattering centre must be
eliminated from the ISAR image via (13) in order to extract the following
brightest scatterer: (13)Ik+1(i)(τ,ν)=Ik(i)(τ,ν)−IPSFk(i)(τ,ν). The algorithm stops when the
energy of the signal component in the ISAR image at the kth iteration is
lower than a given threshold, λ.
Such a threshold is typically set to 5% of the initial energy, that is, the
total energy of the polarimetric ISAR image before any component removal. In
mathematical detail, the preset threshold depends on the energy content and on
the SNR of the initial ISAR image, as detailed in (14) (14)λ=K⋅ESNRSNR+1, where E(I(τ,ν))=∑i=13E(I(i)(τ,ν)), with E(I(i)(τ,ν))=∬|I(i)(τ,ν)|2dτdν.
It is worth pointing out that a coefficient SNR/(SNR+1) is used in order to account for the energy of
the signal component (noiseless image). Moreover, the SNR can be estimated in
the image domain by selecting image areas where no target is present. It must
also be noted that the energy of the signal component of the ISAR image at each
iteration has to be compared to the energy threshold in (14). Therefore, the
iterations stop when Ek(I(τ,ν))(SNR/(SNR+1))<λ.


## 4. Results

The algorithm performance is tested both by using
simulated and real data. The simulation test highlights the algorithm
effectiveness when extracting ideal point-like scatterers, whereas the real
data test shows an example of the output when the Pol-CLEAN is applied to
“real-world” data.


### 4.1. Simulation

The analysis of simulated data aims at testing the
Pol-CLEAN effectiveness when the target is composed of a number of ideal point-like
scatterers with different polarimetric properties. Two separate tests are run.
The first concerns a six-point target with scatterers placed at a distance of 5
resolution cells from each other. The second experiment is proposed to test the
Pol-CLEAN robustness when the point-like scatterers distance drops down to one
resolution cell.


#### 4.1.1. Six-Point Target

AnX-band radar and a six-point target are considered
for the generation of the received signal. Each point is located at a distance
of 5 resolution cells from the others (as shown in Figure 3). The scattering
matrices relative to each point are shown in Table 1, whereas the main radar
parameters are shown in Table 2.Table 1
Scattering centre characteristics.
TypeScattering matrixS1Surface(α=0°)[1001]S2Dihedral(α=90°,β=0°)[100−1]S3Dipole(α=45°,β=45°)[1+2222221−22]S4Dihedral(α=90°,β=30°)[321212−32]S5Surface(α=0°)[1001]S6Dipole(α=45°,β=60°)[32323212]Table 2
Radar parameters.
Central freq. (f0)10 GHzNo. of radar sweeps (N)96Bandwidth (B)400 MHzCross-range res.0.68 mFreq. step (Δf)3.15 MHzRange res.0.375 mNo. of tx freq. (M)128SNR (data domain)−10 dBFigure 3
Six-point target geometry.The simulation is repeated by changing the zero
padding in order to test the algorithm robustness with respect to the image
oversampling. Specifically, zero padding factor (ZPF) of 1, 2, 4, and 8 are
considered (note that ZPF = 1 means “no zero padding”). Gaussian noise has
been added to the raw data in order to have an SNR = −10 dB (in the data
domain).The estimated scattering vectors are decomposed
according to (2) and (3) (only parameters α and β are shown). The estimated type of scattering (α) matches the true values as well as the
estimated orientation angle (β), as shown in Table 3, where the mean value
of the couple of parameters (α, β), obtained by generating 25 noise
realisations, is shown. It is worth noting that the estimated mean values are
weakly affected by the ZPF whereas the standard deviation decreases when the
zero padding increases, as shown in Figure 4, where the root mean square error
(RMSE) of α and β is plotted as a function of the ZPF.Table 3
Estimated scattering parameters.
ZPS1S2S3S4S5S61α55.5°85.99°45.53°86.73°6.55°45.40°β—0.07°45.12°29.88°—61.39°2α5.02°86.64°45.43°86.91°5.64°45.08°β—0.23°45.16°29.51°—61.44°4α5.06°86.56°45.20°86.74°5.52°45.22°β—−0.13°45.13°29.47°—61.52°8α4.97°86.71°45.37°86.96°5.44°45.15°β—−0.09°45.19°29.71°—61.43°Figure 4
Standard deviation versus zero padding factor.The original ISAR images and the ISAR images after the
first and the last scattering centre elimination are shown in Figures5, 6, and
7 for the three Pauli channels, respectively. All ISAR images are obtained by
using ZPF = 8. It is worth noting that the first component removal only affects
the first Pauli channel (HH+VV) since the extracted scatterer has
zero-components in the other two Pauli channels (VV-HH and 2HV) It can be
pointed out that, after the last elimination, the scatterer's contribution is
significantly suppressed.ISAR image on channel HH+VV before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)ISAR image on channel VV-HH before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)ISAR image on channel HV before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)


#### 4.1.2. Robustness Analysis with Respect to Scatterer's Distance

An algorithm performance loss is expected when the
distance between the scatterers reduces. With the present experiment, the
algorithm robustness with respect to the interference caused by the vicinity of
other scatterers is tested. Specifically, two scatterers close to each other
are considered in order to create such an interference. The scatterers chosen
areS1 and S4 (from the previous experiment) and their scattering matrices are
shown in Table 1. Gaussian noise  is added to the generated data in order to obtain a SNR = −10 dB (in the data domain). Both the vicinity along the range and cross-range
coordinate is tested. In particular, the scatterer's distance is varied within
one to five range cells, first along the range direction and then along the
cross-range direction. Figure 8 shows the results in terms of estimation error
for the parameters α and β against the distance in range (as in the
number of range resolution cells), whereas Figure 9 shows the similar results
against the distance in cross-range (as in number of cross-range resolution
cells). The results are shown in terms of the RMSE and they are obtained by
using a ZPF = 8.Figure 8
RMSE against
the distance in range.Figure 9
RMSE against
the distance in cross range.As predicted, the performance of the algorithm
decreases when the distance between scatterers reduces. It can also be pointed
out that the same conclusions are reached when considering range and
cross-range directions. This effect is mainly due to two reasons.(1)
Scatterers interfere with each other because
of their sidelobes. Although it would be tempting to use a window in order to
reduce the sidelobe level, the inconvenient effect of widening the main lobe
would negatively affect the performance when the distance is equal to one
resolution cell.(2)
The cancellation of the scatterer under test
is a nonlinear operation that affects the estimated scattering matrix of the
nearest scatterers.


### 4.2. Real Data

The analysis of real data provides a clear example of
the results achievable when using the Pol-CLEAN. Since no accurate target model
is available, a direct error analysis is not viable for this kind of
experiment. Nevertheless, the results are visually readable by comparing the
extracted scatterers with the Pol-ISAR image.


#### 4.2.1. Data Set Description

The data used for this test is collected during a real
turn-table experiment. The data is obtained from the GTRI publicly releasable
data set. The experiment is run by using a stepped-frequency fully polarimetric
radar system arranged on a tower and looking down to a turn-table. The
illuminated target is a T72 tank. The data file contains 79 radar sweeps for a
fixed elevation angle (θel=29.9994°). After each radar sweep, the turn table is
rotated by 0.05°. Therefore, a total azimuth angle variation of 3.9° is spanned
about the central azimuth angle (θaz=89.231°). The central frequency is equal to f0=9.6 GHz whereas the number of transmitted
frequencies is equal to 221, equally spaced by 3 MHz. The resultant bandwidth is
equal to 660 MHz and both the nominal range and cross-range resolutions are
equal to 0.3048 m.The radar-target geometry is depicted in Figure10,
whereas the target is shown in Figure 11. The radar parameters are shown in
Table 4.Table 4
Radar parameters.
ParametersValuef09.6 GhzFrequency step3 MhzN° transmitted frequencies221N° sweeps79Azimutal sampling rate0.05°Total aspect angle for each file3.9°Nominal range resolution1 footNominal cross-range resolution1 footFigure 10
Radar target
geometry.Figure 11
Target T72.


#### 4.2.2. Real Data Results

The image cross-range section cut across the
scattering centre peak (in blue) and the estimated cross-range section of the
scattering centre PSF (in red) are shown, for all polarimetric channels, in
Figures12, 13, and 14. Moreover, the cross-range section after the scattering
centre removal is shown in green colour. It is worth noting that the estimated
PSF cross-range section is estimated quite accurately, and therefore the
scattering centre is removed from the image. The range section of the same
scattering centre, as well as the range section of the estimated PSF, is shown
in Figures 15, 16, and 17. It can be noted that the results along the range
direction are similar to those along the cross-range direction. Figures 18, 19, 21, 22, 24
and 25 show the ISAR image
before and after the cancellation of the first scatterer, for all
three polarimetric channel. Figures 20, 23, 26 how the ISAR
images after the cancellation of the last scatterer. By setting the energy
threshold defined in (14) to K=0.05,
a number of 43 scatterers are extracted. The RGB ISAR image of the target is
also shown in Figure 27. The colored dots represent the scattering centres
extracted by means of the Pol-CLEAN. The colour of each dot represents the
polarimetric signature of the extracted scattering centre in the Pauli basis.
It should be noted that the colour of the extracted dot is very close to the
colour of the underlying ISAR image, especially in the case of bright
scatterers. Weaker extracted scatterers do not match perfectly the colour of
the underlying ISAR image. This can be explained by considering thatFigure 12
Polarimetric channel HH+VV.Figure 13
Polarimetric channel VV-HH.Figure 14
Polarimetric channel 2HV.Figure 15
Polarimetric channel HH+VV.Figure 16
Polarimetric channel VV-HH.Figure 17
Polarimetric channel 2HV.Figure 18
Original ISAR image—polarimetric channel HH+VV.Figure 19
ISAR image after removing the first scattering centre—polarimetric channel HH+VV.Figure 20
ISAR image after removing the last scattering centre—Polarimetric
channel HH+VV.Figure 21
Original ISAR image—polarimetric channel VV-HH.Figure 22
ISAR image after removing the first scattering centre—polarimetric channel VV-HH.Figure 23
ISAR image after removing the last scattering centre—Polarimetric
channel VV-HH.Figure 24
Original ISAR image—Polarimetric channel 2HV.Figure 25
ISAR image after removing the first scattering centre—polarimetric channel 2VH.Figure 26
ISAR image after removing the last scattering centre—Polarimetric
channel 2HV.Figure 27
RGB ISAR of the target—the colored spots represent
the scatterer extracted by the algorithm.(1)
weaker scatterers are partially masked by stronger
scatterer's sidelobes (it can be read as an interference problem);(2)
even after stronger scatterers are removed, some
residuals remain that affect the extraction of weaker scatterers and therefore
lead to larger estimation errors.Nevertheless, classifiers would weight bright
scatterers more than weak scatterers and therefore such an effect would not
affect the classification performances significantly.


## 4.1. Simulation

The analysis of simulated data aims at testing the
Pol-CLEAN effectiveness when the target is composed of a number of ideal point-like
scatterers with different polarimetric properties. Two separate tests are run.
The first concerns a six-point target with scatterers placed at a distance of 5
resolution cells from each other. The second experiment is proposed to test the
Pol-CLEAN robustness when the point-like scatterers distance drops down to one
resolution cell.


### 4.1.1. Six-Point Target

AnX-band radar and a six-point target are considered
for the generation of the received signal. Each point is located at a distance
of 5 resolution cells from the others (as shown in Figure 3). The scattering
matrices relative to each point are shown in Table 1, whereas the main radar
parameters are shown in Table 2.Table 1
Scattering centre characteristics.
TypeScattering matrixS1Surface(α=0°)[1001]S2Dihedral(α=90°,β=0°)[100−1]S3Dipole(α=45°,β=45°)[1+2222221−22]S4Dihedral(α=90°,β=30°)[321212−32]S5Surface(α=0°)[1001]S6Dipole(α=45°,β=60°)[32323212]Table 2
Radar parameters.
Central freq. (f0)10 GHzNo. of radar sweeps (N)96Bandwidth (B)400 MHzCross-range res.0.68 mFreq. step (Δf)3.15 MHzRange res.0.375 mNo. of tx freq. (M)128SNR (data domain)−10 dBFigure 3
Six-point target geometry.The simulation is repeated by changing the zero
padding in order to test the algorithm robustness with respect to the image
oversampling. Specifically, zero padding factor (ZPF) of 1, 2, 4, and 8 are
considered (note that ZPF = 1 means “no zero padding”). Gaussian noise has
been added to the raw data in order to have an SNR = −10 dB (in the data
domain).The estimated scattering vectors are decomposed
according to (2) and (3) (only parameters α and β are shown). The estimated type of scattering (α) matches the true values as well as the
estimated orientation angle (β), as shown in Table 3, where the mean value
of the couple of parameters (α, β), obtained by generating 25 noise
realisations, is shown. It is worth noting that the estimated mean values are
weakly affected by the ZPF whereas the standard deviation decreases when the
zero padding increases, as shown in Figure 4, where the root mean square error
(RMSE) of α and β is plotted as a function of the ZPF.Table 3
Estimated scattering parameters.
ZPS1S2S3S4S5S61α55.5°85.99°45.53°86.73°6.55°45.40°β—0.07°45.12°29.88°—61.39°2α5.02°86.64°45.43°86.91°5.64°45.08°β—0.23°45.16°29.51°—61.44°4α5.06°86.56°45.20°86.74°5.52°45.22°β—−0.13°45.13°29.47°—61.52°8α4.97°86.71°45.37°86.96°5.44°45.15°β—−0.09°45.19°29.71°—61.43°Figure 4
Standard deviation versus zero padding factor.The original ISAR images and the ISAR images after the
first and the last scattering centre elimination are shown in Figures5, 6, and
7 for the three Pauli channels, respectively. All ISAR images are obtained by
using ZPF = 8. It is worth noting that the first component removal only affects
the first Pauli channel (HH+VV) since the extracted scatterer has
zero-components in the other two Pauli channels (VV-HH and 2HV) It can be
pointed out that, after the last elimination, the scatterer's contribution is
significantly suppressed.ISAR image on channel HH+VV before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)ISAR image on channel VV-HH before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)ISAR image on channel HV before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)


### 4.1.2. Robustness Analysis with Respect to Scatterer's Distance

An algorithm performance loss is expected when the
distance between the scatterers reduces. With the present experiment, the
algorithm robustness with respect to the interference caused by the vicinity of
other scatterers is tested. Specifically, two scatterers close to each other
are considered in order to create such an interference. The scatterers chosen
areS1 and S4 (from the previous experiment) and their scattering matrices are
shown in Table 1. Gaussian noise  is added to the generated data in order to obtain a SNR = −10 dB (in the data domain). Both the vicinity along the range and cross-range
coordinate is tested. In particular, the scatterer's distance is varied within
one to five range cells, first along the range direction and then along the
cross-range direction. Figure 8 shows the results in terms of estimation error
for the parameters α and β against the distance in range (as in the
number of range resolution cells), whereas Figure 9 shows the similar results
against the distance in cross-range (as in number of cross-range resolution
cells). The results are shown in terms of the RMSE and they are obtained by
using a ZPF = 8.Figure 8
RMSE against
the distance in range.Figure 9
RMSE against
the distance in cross range.As predicted, the performance of the algorithm
decreases when the distance between scatterers reduces. It can also be pointed
out that the same conclusions are reached when considering range and
cross-range directions. This effect is mainly due to two reasons.(1)
Scatterers interfere with each other because
of their sidelobes. Although it would be tempting to use a window in order to
reduce the sidelobe level, the inconvenient effect of widening the main lobe
would negatively affect the performance when the distance is equal to one
resolution cell.(2)
The cancellation of the scatterer under test
is a nonlinear operation that affects the estimated scattering matrix of the
nearest scatterers.


## 4.1.1. Six-Point Target

AnX-band radar and a six-point target are considered
for the generation of the received signal. Each point is located at a distance
of 5 resolution cells from the others (as shown in Figure 3). The scattering
matrices relative to each point are shown in Table 1, whereas the main radar
parameters are shown in Table 2.Table 1
Scattering centre characteristics.
TypeScattering matrixS1Surface(α=0°)[1001]S2Dihedral(α=90°,β=0°)[100−1]S3Dipole(α=45°,β=45°)[1+2222221−22]S4Dihedral(α=90°,β=30°)[321212−32]S5Surface(α=0°)[1001]S6Dipole(α=45°,β=60°)[32323212]Table 2
Radar parameters.
Central freq. (f0)10 GHzNo. of radar sweeps (N)96Bandwidth (B)400 MHzCross-range res.0.68 mFreq. step (Δf)3.15 MHzRange res.0.375 mNo. of tx freq. (M)128SNR (data domain)−10 dBFigure 3
Six-point target geometry.The simulation is repeated by changing the zero
padding in order to test the algorithm robustness with respect to the image
oversampling. Specifically, zero padding factor (ZPF) of 1, 2, 4, and 8 are
considered (note that ZPF = 1 means “no zero padding”). Gaussian noise has
been added to the raw data in order to have an SNR = −10 dB (in the data
domain).The estimated scattering vectors are decomposed
according to (2) and (3) (only parameters α and β are shown). The estimated type of scattering (α) matches the true values as well as the
estimated orientation angle (β), as shown in Table 3, where the mean value
of the couple of parameters (α, β), obtained by generating 25 noise
realisations, is shown. It is worth noting that the estimated mean values are
weakly affected by the ZPF whereas the standard deviation decreases when the
zero padding increases, as shown in Figure 4, where the root mean square error
(RMSE) of α and β is plotted as a function of the ZPF.Table 3
Estimated scattering parameters.
ZPS1S2S3S4S5S61α55.5°85.99°45.53°86.73°6.55°45.40°β—0.07°45.12°29.88°—61.39°2α5.02°86.64°45.43°86.91°5.64°45.08°β—0.23°45.16°29.51°—61.44°4α5.06°86.56°45.20°86.74°5.52°45.22°β—−0.13°45.13°29.47°—61.52°8α4.97°86.71°45.37°86.96°5.44°45.15°β—−0.09°45.19°29.71°—61.43°Figure 4
Standard deviation versus zero padding factor.The original ISAR images and the ISAR images after the
first and the last scattering centre elimination are shown in Figures5, 6, and
7 for the three Pauli channels, respectively. All ISAR images are obtained by
using ZPF = 8. It is worth noting that the first component removal only affects
the first Pauli channel (HH+VV) since the extracted scatterer has
zero-components in the other two Pauli channels (VV-HH and 2HV) It can be
pointed out that, after the last elimination, the scatterer's contribution is
significantly suppressed.ISAR image on channel HH+VV before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)ISAR image on channel VV-HH before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)ISAR image on channel HV before any cancellation
(a), after the first cancellation (b), and after the last cancellation
(c).
(a)(b)(c)


## 4.1.2. Robustness Analysis with Respect to Scatterer's Distance

An algorithm performance loss is expected when the
distance between the scatterers reduces. With the present experiment, the
algorithm robustness with respect to the interference caused by the vicinity of
other scatterers is tested. Specifically, two scatterers close to each other
are considered in order to create such an interference. The scatterers chosen
areS1 and S4 (from the previous experiment) and their scattering matrices are
shown in Table 1. Gaussian noise  is added to the generated data in order to obtain a SNR = −10 dB (in the data domain). Both the vicinity along the range and cross-range
coordinate is tested. In particular, the scatterer's distance is varied within
one to five range cells, first along the range direction and then along the
cross-range direction. Figure 8 shows the results in terms of estimation error
for the parameters α and β against the distance in range (as in the
number of range resolution cells), whereas Figure 9 shows the similar results
against the distance in cross-range (as in number of cross-range resolution
cells). The results are shown in terms of the RMSE and they are obtained by
using a ZPF = 8.Figure 8
RMSE against
the distance in range.Figure 9
RMSE against
the distance in cross range.As predicted, the performance of the algorithm
decreases when the distance between scatterers reduces. It can also be pointed
out that the same conclusions are reached when considering range and
cross-range directions. This effect is mainly due to two reasons.(1)
Scatterers interfere with each other because
of their sidelobes. Although it would be tempting to use a window in order to
reduce the sidelobe level, the inconvenient effect of widening the main lobe
would negatively affect the performance when the distance is equal to one
resolution cell.(2)
The cancellation of the scatterer under test
is a nonlinear operation that affects the estimated scattering matrix of the
nearest scatterers.


## 4.2. Real Data

The analysis of real data provides a clear example of
the results achievable when using the Pol-CLEAN. Since no accurate target model
is available, a direct error analysis is not viable for this kind of
experiment. Nevertheless, the results are visually readable by comparing the
extracted scatterers with the Pol-ISAR image.


### 4.2.1. Data Set Description

The data used for this test is collected during a real
turn-table experiment. The data is obtained from the GTRI publicly releasable
data set. The experiment is run by using a stepped-frequency fully polarimetric
radar system arranged on a tower and looking down to a turn-table. The
illuminated target is a T72 tank. The data file contains 79 radar sweeps for a
fixed elevation angle (θel=29.9994°). After each radar sweep, the turn table is
rotated by 0.05°. Therefore, a total azimuth angle variation of 3.9° is spanned
about the central azimuth angle (θaz=89.231°). The central frequency is equal to f0=9.6 GHz whereas the number of transmitted
frequencies is equal to 221, equally spaced by 3 MHz. The resultant bandwidth is
equal to 660 MHz and both the nominal range and cross-range resolutions are
equal to 0.3048 m.The radar-target geometry is depicted in Figure10,
whereas the target is shown in Figure 11. The radar parameters are shown in
Table 4.Table 4
Radar parameters.
ParametersValuef09.6 GhzFrequency step3 MhzN° transmitted frequencies221N° sweeps79Azimutal sampling rate0.05°Total aspect angle for each file3.9°Nominal range resolution1 footNominal cross-range resolution1 footFigure 10
Radar target
geometry.Figure 11
Target T72.


### 4.2.2. Real Data Results

The image cross-range section cut across the
scattering centre peak (in blue) and the estimated cross-range section of the
scattering centre PSF (in red) are shown, for all polarimetric channels, in
Figures12, 13, and 14. Moreover, the cross-range section after the scattering
centre removal is shown in green colour. It is worth noting that the estimated
PSF cross-range section is estimated quite accurately, and therefore the
scattering centre is removed from the image. The range section of the same
scattering centre, as well as the range section of the estimated PSF, is shown
in Figures 15, 16, and 17. It can be noted that the results along the range
direction are similar to those along the cross-range direction. Figures 18, 19, 21, 22, 24
and 25 show the ISAR image
before and after the cancellation of the first scatterer, for all
three polarimetric channel. Figures 20, 23, 26 how the ISAR
images after the cancellation of the last scatterer. By setting the energy
threshold defined in (14) to K=0.05,
a number of 43 scatterers are extracted. The RGB ISAR image of the target is
also shown in Figure 27. The colored dots represent the scattering centres
extracted by means of the Pol-CLEAN. The colour of each dot represents the
polarimetric signature of the extracted scattering centre in the Pauli basis.
It should be noted that the colour of the extracted dot is very close to the
colour of the underlying ISAR image, especially in the case of bright
scatterers. Weaker extracted scatterers do not match perfectly the colour of
the underlying ISAR image. This can be explained by considering thatFigure 12
Polarimetric channel HH+VV.Figure 13
Polarimetric channel VV-HH.Figure 14
Polarimetric channel 2HV.Figure 15
Polarimetric channel HH+VV.Figure 16
Polarimetric channel VV-HH.Figure 17
Polarimetric channel 2HV.Figure 18
Original ISAR image—polarimetric channel HH+VV.Figure 19
ISAR image after removing the first scattering centre—polarimetric channel HH+VV.Figure 20
ISAR image after removing the last scattering centre—Polarimetric
channel HH+VV.Figure 21
Original ISAR image—polarimetric channel VV-HH.Figure 22
ISAR image after removing the first scattering centre—polarimetric channel VV-HH.Figure 23
ISAR image after removing the last scattering centre—Polarimetric
channel VV-HH.Figure 24
Original ISAR image—Polarimetric channel 2HV.Figure 25
ISAR image after removing the first scattering centre—polarimetric channel 2VH.Figure 26
ISAR image after removing the last scattering centre—Polarimetric
channel 2HV.Figure 27
RGB ISAR of the target—the colored spots represent
the scatterer extracted by the algorithm.(1)
weaker scatterers are partially masked by stronger
scatterer's sidelobes (it can be read as an interference problem);(2)
even after stronger scatterers are removed, some
residuals remain that affect the extraction of weaker scatterers and therefore
lead to larger estimation errors.Nevertheless, classifiers would weight bright
scatterers more than weak scatterers and therefore such an effect would not
affect the classification performances significantly.


## 4.2.1. Data Set Description

The data used for this test is collected during a real
turn-table experiment. The data is obtained from the GTRI publicly releasable
data set. The experiment is run by using a stepped-frequency fully polarimetric
radar system arranged on a tower and looking down to a turn-table. The
illuminated target is a T72 tank. The data file contains 79 radar sweeps for a
fixed elevation angle (θel=29.9994°). After each radar sweep, the turn table is
rotated by 0.05°. Therefore, a total azimuth angle variation of 3.9° is spanned
about the central azimuth angle (θaz=89.231°). The central frequency is equal to f0=9.6 GHz whereas the number of transmitted
frequencies is equal to 221, equally spaced by 3 MHz. The resultant bandwidth is
equal to 660 MHz and both the nominal range and cross-range resolutions are
equal to 0.3048 m.The radar-target geometry is depicted in Figure10,
whereas the target is shown in Figure 11. The radar parameters are shown in
Table 4.Table 4
Radar parameters.
ParametersValuef09.6 GhzFrequency step3 MhzN° transmitted frequencies221N° sweeps79Azimutal sampling rate0.05°Total aspect angle for each file3.9°Nominal range resolution1 footNominal cross-range resolution1 footFigure 10
Radar target
geometry.Figure 11
Target T72.


## 4.2.2. Real Data Results

The image cross-range section cut across the
scattering centre peak (in blue) and the estimated cross-range section of the
scattering centre PSF (in red) are shown, for all polarimetric channels, in
Figures12, 13, and 14. Moreover, the cross-range section after the scattering
centre removal is shown in green colour. It is worth noting that the estimated
PSF cross-range section is estimated quite accurately, and therefore the
scattering centre is removed from the image. The range section of the same
scattering centre, as well as the range section of the estimated PSF, is shown
in Figures 15, 16, and 17. It can be noted that the results along the range
direction are similar to those along the cross-range direction. Figures 18, 19, 21, 22, 24
and 25 show the ISAR image
before and after the cancellation of the first scatterer, for all
three polarimetric channel. Figures 20, 23, 26 how the ISAR
images after the cancellation of the last scatterer. By setting the energy
threshold defined in (14) to K=0.05,
a number of 43 scatterers are extracted. The RGB ISAR image of the target is
also shown in Figure 27. The colored dots represent the scattering centres
extracted by means of the Pol-CLEAN. The colour of each dot represents the
polarimetric signature of the extracted scattering centre in the Pauli basis.
It should be noted that the colour of the extracted dot is very close to the
colour of the underlying ISAR image, especially in the case of bright
scatterers. Weaker extracted scatterers do not match perfectly the colour of
the underlying ISAR image. This can be explained by considering thatFigure 12
Polarimetric channel HH+VV.Figure 13
Polarimetric channel VV-HH.Figure 14
Polarimetric channel 2HV.Figure 15
Polarimetric channel HH+VV.Figure 16
Polarimetric channel VV-HH.Figure 17
Polarimetric channel 2HV.Figure 18
Original ISAR image—polarimetric channel HH+VV.Figure 19
ISAR image after removing the first scattering centre—polarimetric channel HH+VV.Figure 20
ISAR image after removing the last scattering centre—Polarimetric
channel HH+VV.Figure 21
Original ISAR image—polarimetric channel VV-HH.Figure 22
ISAR image after removing the first scattering centre—polarimetric channel VV-HH.Figure 23
ISAR image after removing the last scattering centre—Polarimetric
channel VV-HH.Figure 24
Original ISAR image—Polarimetric channel 2HV.Figure 25
ISAR image after removing the first scattering centre—polarimetric channel 2VH.Figure 26
ISAR image after removing the last scattering centre—Polarimetric
channel 2HV.Figure 27
RGB ISAR of the target—the colored spots represent
the scatterer extracted by the algorithm.(1)
weaker scatterers are partially masked by stronger
scatterer's sidelobes (it can be read as an interference problem);(2)
even after stronger scatterers are removed, some
residuals remain that affect the extraction of weaker scatterers and therefore
lead to larger estimation errors.Nevertheless, classifiers would weight bright
scatterers more than weak scatterers and therefore such an effect would not
affect the classification performances significantly.


## 5. Conclusions

Scattering centre extraction from polarimetric ISAR
images can be achieved by extending the CLEAN technique, which was designed to
perform scattering centre extraction from single polarization ISAR images. The
extension of the CLEAN technique, namely, the Pol-CLEAN technique has been
first proposed in this paper and then tested on simulated and real data. The
results have shown that the Pol-CLEAN technique is able to extract scattering
centres from noisy ISAR images and estimate their locations and polarisation
vectors. A table with essential information is then obtained that contains only
the positions and polarimetric vectors of the extracted scatterers, which can
be used as a feature set for automated target classification and recognition.



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*Source: 325279-2008-08-12.xml*