Super-resolution Doppler beam sharpening
imaging via sparse representation
ISSN 1751-8784
Received on 14th February 2015
Revised on 4th September 2015
Accepted on 20th September 2015
doi: 10.1049/iet-rsn.2015.0094
www.ietdl.org
Hongmeng Chen
1
✉
, Ming Li
1
, Zeyu Wang
1
, Yunlong Lu
1
, Shuai Wang
1
, Lei Zuo
1
, Peng Zhang
1
,
Yan Wu
2
1
National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, Shaanxi, People’s Republic of China
2
School of Electronics Engineering, Xidian University, Xi’an 710071, Shaanxi, People’s Republic of China
✉ E-mail: chenhongmeng123@163.com
Abstract: In Doppler beam sharpening (DBS) imaging, the imaging scene is characterised corresponding to the Doppler
band, and the Doppler band occupies only a small part compared with the whole frequency domain. A ccordingly, the
DBS image is sparse in the frequency domain. Motivated by the sparsity, the authors propose a novel framework of
DBS formation via sparse representation to perform super-resolution. In the framework, by exploiting the fact that the
ground scene is sparse in frequency domain, they perform the super-resolution formation by incorporating the sparsity
constraint with respect to a redundant time–frequency dictionary. The recovered sparse coefficients are utilised to form
the final DBS image in frequency domain. Since the dictionary is redundant with more columns than rows, a thinner
Doppler frequency resolution and a higher sharpening ratio can be achieved. Experimental results on real measured
data verify the effectiveness of the new super-resolution algorithm.
1 Introduction
Nowadays, for airborne radar systems, the wide-area surveillance
ability is more and more important, which can be realised through
antenna scanning in a periodic manner. To accurately estimate the
azimuth positions of objects, the azimuth beam width of the radar
antenna has to be narrow. Doppler beam sharpening (DBS)
technique is a technique to obtain an oval picture of the scanned
scene [1, 2] widely applied to battlefield surveillance and traffic
monitoring [3, 4]. However, its sharpening ratio (i.e. Doppler
frequency resolution) is always limited. Especially, in order to
achieve a high revisit and wide-area surveillance ability, the
illumination time of beam at each single azimuth position cannot
be very long; accordingly, the sharpening ratio is not very high.
Therefore, it is of great importance to study the super-resolution
for DBS imaging further.
In general, the high resolution in range direction is realised by
transmitting a wideband signal, while the resolution in azimuth
direction is realised by the Doppler spectral analysis. High
sharpening ratio of a DBS image is achievable when enough
pulses are measured, since a longer coherent processing interval
(CPI) in time domain corresponds to a thinner frequency
resolution in frequency domain. For an airborne radar system, the
wide-area surveillance ability can be achieved by steering the
antenna from one azimuth angle to another periodically, as is
shown in Fig. 1a. On the one hand, in order to guarantee high
revisit rate and wide-area surveillance ability, the radar has to
work in a scanning mode. Therefore, the observation time of each
beam at different azimuth angles is quite finite, which means that
the CPI cannot be very long and the collected pulses are very few.
On the other hand, a long CPI data collection (i.e. a large coherent
pulse number) can ensure a high sharpening ratio, since the
sharpening ratio is inversely proportional to the synthesised
observation time. However, for traditional DBS imaging method,
for example, Fourier transform-based algorithm [5, 6], high
sharpening ratio is unachievable when the number of pulses is
limited.
The conflict between CPI and sharpening ratio in DBS imaging
motivates us to perform super-resolution. Super-resolution has
drawn a lot of attention in recent years, which include target
super-resolution of point-sources [7, 8] and image super-resolution
from multiple frames [9]. For DBS imaging, super-resolution is
performed based on only single frame image corresponding to one
azimuth position [5, 6]. Modern spectral estimation technique
based on RELAX algorithm is discussed in [10]. In [11], an
AE-CSR algorithm is introduced, aperture extrapolation technique
is utilised to increase the data length in azimuth direction and the
amplitude and phase estimation of a sinusoid is applied to replace
the fast Fourier transform (FFT) to perform the Doppler analysis.
The new emerging theory of compressive sensing (CS) states that
a sparse signal can be reconstructed from highly incomplete
samples or measurements [12]. The CS theory has shown good
prospects in radar applications when the interest scene is sparse in
some observed domain [13], and which has been successfully used
in target separation of point-sources [7, 8], image denoising [14],
synthetic aperture radar imaging [15, 16], inversed synthetic
aperture radar imaging [17–19
], direction of arrival estimation [20]
and range spread target detection of wideband radar [21]. Inspired
by above works, we consider the sparse representation (SR) of
DBS image formation, and focus on performing the super-resolution.
In this paper, we will propose an alternative framework of DBS
super-resolution formation using SR (SR-DBS). Since the useful
scene information for DBS image is always corresponding to the
Doppler band, and the Doppler band distributes just part in the
whole frequency domain [1, 2, 5, 11], the DBS image is
intrinsically sparse in frequency domain. This distribution of
Doppler band provides a sparsity feature of the DBS image.
Therefore, it is possible to enhance the sharpening ratio using the
sparsity of the DBS image. In this paper, we tend to exploit the
sparsity and include it as the constraint term to provide a prior
for the purpose of super-resolution. In our SR-DBS framework,
we construct a redundant time–frequency dictionary with more
columns than rows to thin the Doppler resolution and extract the
complex amplitudes of scattering centres to form the final DBS
image. Benefiting from the sparse constraint and constructed
redundant time–frequency dictionary, a thinner frequency
resolution can be realised, and a higher sharpening ratio can be
achieved. Real data experiments confirm that the proposed
scheme can provide a super-resolution imaging result for airborne
radar.
IET Radar, Sonar & Navigation
Research Article
IET Radar Sonar Navig., 2016, Vol. 10, Iss. 3, pp. 442–448
442
&
The Institution of Engineering and Technology 2016