close

Вход

Забыли?

вход по аккаунту

?

s12524-017-0709-3

код для вставкиСкачать
J Indian Soc Remote Sens
DOI 10.1007/s12524-017-0709-3
RESEARCH ARTICLE
2D Superresolution ISAR Imaging via Temporally Correlated
Multiple Sparse Bayesian Learning
Xiaowei Hu1 • Ningning Tong1 • Xingyu He1 • Yuchen Wang1
Received: 7 April 2016 / Accepted: 1 September 2017
Ó Indian Society of Remote Sensing 2017
Abstract In inverse synthetic aperture radar (ISAR)
imaging, the image resolution is always limited by the
bandwidth and the observation time. Sparse recovery (SR)
is recently proposed to improve the range resolution or
cross-range resolution effectively. However, for the two
dimensional superresolution case, a SR-induced range cell
migration (RCM) occurs among the High-Resolution
Range Profiles (HRRPs) and definitely degrades the ISAR
image. After that translational motion compensation is
completed, the common sparsity of HRRPs is exploited to
suppress the RCM in this paper. Furthermore, by taking the
temporal correlation of HRRPs into account, an ISAR
imaging method based on temporally correlated Multiple
Sparse Bayesian Learning is proposed to improve the
imaging quality. Simulated data and real data results
demonstrate the effectiveness of the proposed method.
Keywords Inverse synthetic aperture radar 2D
superresolution Sparse recovery Temporally correlated
Multiple Sparse Bayesian Learning
Introduction
In inverse synthetic aperture radar (ISAR) imaging, the
range-Doppler image is usually obtained by using two-dimensional (2D) fast Fourier transform (FFT). However, the
2D resolution is always limited by the bandwidth and the
rotation angle during the observation time. Considering the
sparsity of target image, sparse recovery (SR) method is
& Xiaowei Hu
huxiaowei1987625@163.com
1
Air Force Engineering University, Xi’an 710051, China
recently proposed to improve the range resolution (Wang
et al. 2011; Zhu et al. 2011; Zhang et al. 2011) or crossrange resolution (Xu et al. 2011; Liu et al. 2014). And
some fine SR methods, such as the Sparse Bayesian
Learning (SBL) (Wipf and Rao 2004), prove to be capable
of obtaining satisfactory resolution with limited bandwidth
and short observing time. However, a problem will emerge
when SR is used for the 2D superresolution. In the highresolution range profile (HRRP) synthesis using SR, a
problem called range cell migration (RCM) (Gao et al.
2015) will arise in the HRRPs, especially for the case of
complex targets imaging. This irregular RCM will seriously influence cross-range profile synthesis using SR and
obviously deteriorate the ISAR image finally. The RCM,
mainly caused by the problem of basis mismatch (Chi et al.
2011) in SR, cannot be addressed by the conventional
compensation methods which are aiming at the migration
through resolution cells (MTRC). Gao et al. (2015) propose
a skillful SR-based imaging framework to avoid the RCM
effectively, however, it may produce several false scatters
and will degrade the final image in some degree.
Assuming that the translational motion has been already
compensated, the signal of targets should retain the common profile in the HRRPs domain. It means that the
position of nonzero components will not change, i.e.,
HRRPs hold the common sparsity (Cotter et al. 2005). In
this paper, a refined SBL method considering the common
sparsity, is used to restrain the RCM. It is called the temporally correlated Multiple Sparse Bayesian Learning
(TMSBL) (Zhang et al. 2011). By exploiting the common
sparsity, the irregular RCM is expected to be aligned in the
HRRP synthesis. Furthermore, components in each nonzero row of HRRPs are usually temporally correlated.
However, most of existing SR algorithms (Cotter et al.
2005; Zhang et al. 2011) all ignore the temporal correlation
123
J Indian Soc Remote Sens
and assume that components are independent and identically distributed (i.i.d.). All of them result in the degraded
HHRPs. TMSBL models the temporal correlation using a
block sparse Bayesian learning framework, and can obtain
a better recovery performance than other algorithms in the
case of temporal correlation. Therefore, a improved ISAR
image can be achieved by using TMSBL.
the noise vector and the expected HRRP in the nth
observing angle, respectively. Then Eq. (1) can be rewritten in a matrix form
S ¼ s0 ; . . .; sn ; . . .; sðN1Þ
¼ U h0 ; . . .; hn ; . . .; hðN1Þ þ e0 ; . . .; en ; . . .; eðN1Þ
¼ UH þ E
ð2Þ
ISAR Signal Model
In ISAR echo model, the radar target is usually considered
in the far-field and is composed of finite scattering centers
with different scattering coefficients. Thus, the echo signal
from a radar target can be seen as the sum of complex
scattered signals from each scattering center. In this paper,
we consider that the echo is collected in a short interval and
the small angle approximation holds. Then the echo signal
of a target with Q scatterers can be expressed as (Wang
et al. 2015)
sðm; nÞ ¼
Q
X
rq exp j4p=c fmx xq þ fny yq þ eðm; nÞ:
q¼1
ð1Þ
where m ¼ 0; 1; . . .; M 1, n ¼ 0; 1; . . .; N 1. rq denotes
the scattering coefficient of the qth scatterer with a coordinate of ðxq ; yq Þ. c is the propagation speed of the wave.
fmx ffi fm ¼ m df , fny ffi fc hn ¼ fc ndh, are the sampling
results in the frequency domain and the angle domain. df ,
dh are the frequency step and angle step, respectively. fc
denotes the center frequency. eðm; nÞ denotes the additional
white Gaussian noise with zero mean. By applying the 2D
FFT to the above signal, an ISAR image of the target can
be obtained. However, due to the narrow bandwidth and
the short observing interval, the resolution of the image is
usually not satisfactory in both the range direction and
cross-range direction.
where S 2 CMN , E 2 CMN , H 2 CMN denote the signal
matrix, noise matrix, and the HRRPs matrix, respectively.
U 2 CMM is a partial Fourier matrix, which is defined as
2
3
1
1
1
Þ
11
1ðM1
61
7
X
X
7
..
..
..
U¼6
4 ...
5
.
.
.
XðM1Þ1 XðM1ÞðM1Þ
where X ¼ exp j 2p
. For the superresolution case, M
M
should be bigger than M.
Now the common sparsity of HRRPs is modelled by
row of H a Gaussian prior
assigning to the mth
1
¼ 0; 1; . . .; M
pðHm
m
ð3Þ
; cm ; RÞ N ð0; cm RÞ;
1
where cm is an unknown variance parameter controlling the
row sparsity in H, and R is a positive definite matrix that
captures the temporal correlation of H. Then Eq. (2) can be
re-expressed in vector form
h þ e
s ¼ U
ð4Þ
where
s ¼ vecðST Þ,
h ¼ vecðHT Þ,
e ¼ vecðET Þ,
¼ U I N , vecðÞ denotes the vectoring operation, and U
denotes the Kronecker product. Suppose that elements in
the noise vector e are independent and each is Gaussian
with noise variance k. Then the Gaussian likelihood of (4)
is given
p sh; k N ðUh; kI Þ
ð5Þ
The prior of common sparsity can be vectorized as
cm ; R; 8m
N ð0; C RÞ
p h;
ð6Þ
TMSBL-Based ISAR Imaging
In this paper, a new ISAR imaging method based on
TMSBL is proposed to improve the 2D ISAR resolution.
This method consists of two steps: the HHRP synthesis via
TMSBL and ISAR imaging via SBL, which will be discussed in the following.
HHRP Synthesis
Let sn ¼ ½sð0; nÞ; . . .; sðM 1; nÞTM1 , en ¼ ½eð0; nÞ; . . .;
eðM 1; nÞTM1 , and hn 2 CM1 denote the signal vector,
123
where C ¼ diagðc0 ; c1 ; . . .; cM1
Þ. By combining the likelihood and the prior above, we can get the posterior density
of h which is also Gaussian
N lh; Rh
p hjs; k; cm ; R; 8m
ð7Þ
where
T s k
lh ¼ RhU
h
i1
TU
k
Rh ¼ ðC RÞ1 þU
ð8Þ
ð9Þ
J Indian Soc Remote Sens
With
a
reasonable
approximation
1
1 1
T
T
ðC RÞU
kI þ UCU
R
(Zhang
kI þ U
and Rao 2011), Eqs. (8) and (9) can be simplified as
1
ð10Þ
lH ¼ CUT kI þ UCUT S
1
ð11Þ
RH ¼ C1 þ UT U k
Hyperparameters k; C; R can be estimated with the
Type-II maximum likelihood which marginalizes over the
weights and then performs the maximum-likelihood estimation. The estimated results are shown below
1 T 1
cm ¼
H R Hm
ð12Þ
þ ðRH Þmm ; 8m
N m
h
i
T
T 1
kS UHk2F kTr UCU kI þ UCU
ð13Þ
þ
k¼
M
MN
~
R
R¼ ;
R
~
where
~¼
R
F
M1
X
HTm
cm
Hm
ð14Þ
Experimental Section
Simulated Data Experiments
m¼0
where TrðÞ denotes the trace of a matrix. An iterative
procedure is produced by the learning rules Eqs. (10), (11),
(12), (13) and (14), with which all hyperparameters can be
estimated, and the maximum a posterior (MAP) estimate of
H can be obtained, too. Thus, the HRRPs without RCM
can be synthesized in this step.
ISAR Imaging
The next step aims to achieve the superresolution in the
cross-range direction and get the high resolution ISAR
image finally. This process can be formulated as an optimization problem
x^m ¼ arg min khm Wxm k2 þskxm k1
ð15Þ
x^m CN
where kk1 denotes the l1 norm of a vector. hm ¼ HTm
th range cell of the
denotes the signal vector in the m
HRRPs. X 2 CMN denotes the high resolution ISAR
th range cell.
image, and xm ¼ X Tm
is the vector in the m
NN
s is
is the partial Fourier matrix, where N\N.
W2C
the regularized factor. Equation (15) can be solved by
Fig. 1 Flow charts of different
methods. a SBL-based method;
b TMSBL-based method
using the SBL algorithm. One can find the details of SBL’s
application in superresolution in the paper of Liu et al.
(2014). After applying SBL in each range cell, the high
resolution ISAR image can be achieved finally.
The main difference between the proposed method and
the conventional SR method is focused on the range
compression, in which TMSBL is adopted for the proposed
method, while SBL is adopted for the conventional one. In
conclusion, the process flow of the proposed method is
depicted in Fig. 1b. And the conventional SR method
(using SBL algorithm for both range and cross-range
compression) is given in Fig. 1a for comparison. In the
following, the above two methods are called the SBL and
TMSBL-based method, respectively.
A simulated data of Boeing 727, which is downloaded from
an online source (http://airborne.nrl.navy.mil/vchen/tftsa.
html), is used in this simulation. Radar parameters of this
data are shown in Table 1. Motion compensation is completed originally. In the experiment, a partial successive
data with the size of 64 64 is utilized to test the 2D
superresolution performance of the proposed method. The
expected 2D superresolution image is with the size of
128 128. Some existing methods of 2D IFFT, SBL and
FSI in the paper of Gao et al. (2015) are used for comparison. The results (HRRPs and ISAR image) under the
signal-to-noise rate (SNR) 30 dB are shown in Fig. 2. We
can see from Fig. 2a, b that, the conventional IFFT method
results in blurred dominant scatters, duo to the limited
bandwidth and coherent time. Figure 2c, d show the results
Table 1 Parameters of online data
Carrier
frequency
(GHz)
Waveform
bandwidth
(MHz)
Radar
PRF
(KHz)
No. of
bursts
Data
length
9
150
20
64
64 9 256
HRRPs
Radar
echo
Motion
compensation
SBL
SBL
ISAR
image
SBL
ISAR
image
a
HRRPs
Radar
echo
Motion
compensation
TMSBL
b
123
J Indian Soc Remote Sens
120
20
100
Range cell
40
Range cell
Fig. 2 Simulated data results.
a HRRPs via IFFT; b ISAR
image via IFFT; c HRRPs via
SBL; d ISAR image via SBL;
e HRRPs via FSI; f ISAR image
via FSI; g HRRPs via TMSBL;
h ISAR image via TMSBL
60
80
80
60
40
100
20
120
10
20
30
40
50
60
20
40
Pulse-train index
60
80
100
120
100
120
100
120
100
120
Cross-range cell
a
b
120
20
100
Range cell
Range cell
40
60
80
80
60
40
100
20
120
10
20
30
40
50
60
20
Pulse-train index
40
60
80
Cross-range cell
c
d
120
20
Range cell
Range cell
100
40
60
80
80
60
40
100
20
120
20
40
60
80
100
20
120
40
60
80
Cross-range cell
Pulse-train index
e
f
120
20
Range cell
Range cell
100
40
60
80
80
60
40
100
20
120
10
20
30
40
Pulse-train index
g
123
50
60
20
40
60
80
Cross-range cell
h
J Indian Soc Remote Sens
ðl;nÞ2RT
35
IFFT
30
SBL
25
TMSBL
FSI
TBR
using SBL method. Obvious RCM arises in the HRRPs and
many false scatters exist in the final image. Results using
FSI and the proposed method are shown in Fig. 2e–h,
respectively. We can see in Fig. 2e, g that, RCMs can be
effectively restrained using both FSI and TMSBL. What is
more, the proposed method produces less sidelobes than
FSI, which is shown in Fig. 2f, h. It preliminarily
demonstrates the superiority of the proposed method.
Furthermore, the above methods are tested under different noise level. To measure the performance quantificationally, the target-to-background ratio (TBR) is defined
by
0
1
,
X
X
2
2
TBR ¼ 10 log 10@
jXðl; nÞj
jXðl; nÞj A
20
15
10
5
0
0
where X denotes the recovered ISAR image, RT and RB are
the predetermined target and background regions, respectively. TBR measures the target energy preservation and
can reflect the quality of the recovered ISAR image. The
higher quality the image is, the higher TBR is. In order to
get the target and background regions, we apply 128 128
points 2D IFFT to the full data instead of the partial data,
and a high-quality ISAR image can be obtained. 2D
median filtering is applied to the ISAR image and four
times the mean value of all pixels is set as the threshold to
separate the target region and the background region.
Points located within the target region RT are regarded as
true signal, and the rest are noise. After counting the target
energy (within the target region) and noise energy (within
the background region) of the reconstructed image, the
target-to-background ratio is obtained. TBRs of different
methods with SNR = 0:5:40 dB are shown in Fig. 3. We
can see that the proposed method holds the highest TBR
under various SNRs among all the methods.
20
30
40
SNR(dB)
ðl;nÞ2RB
ð16Þ
10
Fig. 3 Experimental results with different SNRs
and 128 complex samples are used. 2D IFFT, SBL, FSI and
TMSBL methods are applied to obtain a superresolution
image with the size of 256 128. The experimental results
are shown in Fig. 4. Because of the shortage of data length,
only a low resolution ISAR image is got via the IFFT
method. The SBL method can improve the resolution but
with a RCM problem. The FSI method is able to alleviate
the RCM in HRRPs, however, it produces some false
scatters in the ISAR image. The proposed method results in
a well-focused ISAR image while alleviating the RCM in
HRRPs. All these prove the better performance of our
method.
In Table 2, TBR of ISAR images via different methods
are given to compare the image quality quantitatively. The
full-data ISAR image is obtained by applying 256 128
points 2D IFFT to the full real data of YaK-42 plane
Obviously, the image via TMSBL holds the highest TBR
value, which suggests the superiority of our proposed
method over other existing methods in real applications.
Real Data Experiments
In this part, a set of real data of the Yak-42 plane is used to
test the performance of the proposed method. The signal
bandwidth is 400 MHz with carrier frequency 10 GHz,
which is corresponding to a range resolution of 0.375 m.
The pulse repetition frequency is 100 Hz. 128 successive
pulses are saved and 256 complex samples are collected for
each pulse. The translational motion has been compensated
with existing method for this data set. In the superresolution experiment, a limited data with 64 successive pulses
Conclusion
In this paper, a TMSBL-based method is proposed to
enhance the 2D resolution of ISAR image. After motion
compensation, accurate HRRPs can be obtained by
exploiting the common sparsity and the temporal correlation. An improved ISAR image is generated by aligning the
SR-induced RCM successfully. Experiment results verify
the effectiveness of the proposed method.
123
J Indian Soc Remote Sens
250
50
200
Range cell
Range cell
Fig. 4 Real data results.
a HRRPs via IFFT; b ISAR
image via IFFT; c HRRPs via
SBL; d ISAR image via SBL;
e HRRPs via FSI; f ISAR image
via FSI; g HRRPs via TMSBL;
h ISAR image via TMSBL
100
150
200
150
100
50
250
10
20
30
40
50
60
20
Pulse-train index
40
60
80
100
120
100
120
100
120
100
120
Cross-range cell
a
b
250
200
Range cell
Range cell
50
100
150
200
150
100
50
250
10
20
30
40
50
60
20
Pulse-train index
40
60
80
Cross-range cell
c
d
250
200
Range cell
Range cell
50
100
150
200
150
100
50
250
20
40
60
80
100
120
20
Pulse-train index
40
60
80
Cross-range cell
e
f
250
200
Range cell
Range cell
50
100
150
200
150
100
50
250
10
20
30
40
Pulse-train index
g
123
50
60
20
40
60
80
Cross-range cell
h
J Indian Soc Remote Sens
Table 2 ISAR image quality
Method
IFFT
SBL
FSI
TMSBL
TBR
11.6555
10.9478
13.3470
20.4262
Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos. 61701526, 61372166,
61571459).
References
Chi, Y., Scharf, L., Pezeshki, A., & Calderbank, A. R. (2011).
Sensitivity to basis mismatch in compressed sensing. IEEE
Transactions on Signal Processing, 59(5), 2182–2195.
Cotter, S., Rao, B., Engan, K., & Kreutz-Delgado, K. (2005). Sparse
solutions to linear inverse problems with multiple measurement
vectors. IEEE Transactions on Signal Processing, 53(7),
2477–2488.
Gao, X., Liu, Z., Chen, H., & Li, X. (2015). Fourier-sparsity
integrated method for complex target ISAR imagery. Sensors,
15(2), 2723–2736.
Liu, H., Jiu, B., & Liu, H. (2014). Superresolution ISAR imaging
based on sparse bayesian learning. IEEE Transactions on
Geoscience and Remote Sensing, 52(8), 5005–5013.
Wang, H., Quan, Y., & Xing, M. (2011). ISAR imaging via sparse
probing frequency. IEEE Geoscience and Remote Sensing
Letters, 8(3), 451–455.
Wang, X., Zhang, M., & Zhao, J. (2015). Super-resolution ISAR
imaging via 2D unitary ESPRIT. Electronics Letters, 51(6),
519–521.
Wipf, D. P., & Rao, B. D. (2004). Sparse Bayesian learning for basis
selection. IEEE Transactions on Signal Processing, 52(8),
2153–2164.
Xu, G., Xing, M., & Zhang, L. (2011). Bayesian inverse synthetic
aperture radar imaging. IEEE Geoscience and Remote Sensing
Letters, 8(6), 1150–1154.
Zhang, L., Qiao, Z., & Xing, M. (2011). High-resolution ISAR
imaging with sparse stepped-frequency waveforms. IEEE Transactions on Geoscience and Remote Sensing, 49(11), 4630–4651.
Zhang, Z., & Rao, B. (2011). Sparse signal recovery with temporally
correlated source vectors using sparse Bayesian learning. IEEE
Journal of Selected Topics in Signal Processing, 5(5), 912–926.
Zhu, F., Zhang, Q., & Lei, Q. (2011). Reconstruction of moving
target’s HRRP using sparse frequency-stepped chirp signal.
IEEE Sensors Journal, 11(10), 2327–2334.
123
Документ
Категория
Без категории
Просмотров
5
Размер файла
1 356 Кб
Теги
0709, 017, s12524
1/--страниц
Пожаловаться на содержимое документа