Signal Processing - November 2016 - 100

estimated in one stage can lead to a
and K is the number of moving targets.
Compared to the
degraded performance in the subsequent
As described previously, the dictionary
deterministic sparsitystages. In the discussed framework, the
A (c 1, ..., c K ) ! C P # KN is a n overcominducing framework,
signal estimation is conducted in a statisplete one. It is constructed by concatestatistical sparsity-based
tical manner, where the obtained statisnating K subdictionaries, where each
techniques provide
tics indicate the uncertainty in the signal
subdictionary is constructed by an LFM
estimation. Therefore, the estimation
matrix with chirp rate c i . In [54], a
new opportunities to
could be more accurate.
scaled Gaussian mixture distribution is
significantly improve the
By properly manipulating the statistical
used to model sparsity. Similar to the
performance of
sparsity models, a performance gain can
work covered in the "Statistical Sparsityradar imagery.
be obtained.
Based Autofocus Techniques in Radar
Imagery" section, statistical information
is utilized to estimate the error parameter E and the chirp
Future directions
rate c i, where the error propagation problem during iteraSince the statistical sparsity-based methods are quite attraction is reduced [47], [54].
tive, it would be most interesting to investigate the following
In Figure 10, the canonical Gotcha data set is used for
problems in the future.
validation, and an example of the Durango target image is
■ Computational complexity. The statistical sparsity-based
given to demonstrate the performance. Due to the movement
methods operate in an iterative manner, where the numof the target, the original image is substantially blurred, as
ber of iterations and the computational cost of each iteraobserved in Figure 10(a). After representing the received sigtion determine the total computational cost. Compared to
nal by the LVD, the , 1-norm regularization method and the
the conventional Fourier-based approach for radar
imaging, the computational complexity is much higher. It
conventional sparse Bayesian method are applied to obtain
is therefore imperative to develop fast algorithms that
the moving target images, as shown in Figure 10(b) and
could decrease the computational complexity or obtain
(c), respectively. The , 1-regularized method and the sparse
fast convergence. The fast algorithms would be particuBayesian method cannot properly focus the target image due
larly useful for many radar applications requiring realto the representation error in the LVD. In contrast, the statistime processing.
tical sparsity-based method with refinement leads to the best
imaging performance in terms of better concentration and
■ Motion compensation errors. In high-resolution radar
desirable noise suppression, as shown in Figure 10(d). The
imaging, a large CPI is required. Then the target movement
superior performance of the statistical sparsity-based methbecomes a problem as the radar line-of-sight dramatically
od is also evaluated quantitatively by the calculated entropy
changes. In such a scenario, even after carrying out coarse
and target-to-clutter ratio (TCR) as shown in Figure 10. In
motion compensation, RCM and phase error would still be
particular, the target image is focused within a 5 m # 5 m
present in the radar echoes. Then, the dictionary allowing
sparse representation would become more complicated,
area that is in accordance with the Durango truth with a size
where the proposed imaging algorithm should also be able
of 5 m # 2 m.
to correct RCM and phase errors. The main challenge is to
properly obtain the approximated solution in the presence
Summary and future directions
of a more complicated model. Toward this end, it would be
particularly suitable to exploit statistical sparsity to limit
Summary
error propagation. One possible way of coping with this
Sparsity-based techniques have been reviewed from a stachallenge is to encode priors on the error parameters to
tistical perspective, along with their recent advances in
properly regularize the solution space.
radar imagery. Various applications show that improved
performance can be obtained by adequately utilizing a sta■ Temporal correlation in SAR GMTIm. Conventionally,
tistical sparse model. The improvements obtained in the
most SAR GMTIm algorithms focus on image formareviewed applications were largely dependent on the foltion of the moving target at one particular time instant.
lowing core ingredients:
However, it is important to also monitor the movement
of the moving target. Since the target's motion and
■ Probabilistic modeling by incorporating flexible priors
imaging background are time-varying, simply generatin the signal is one of the most remarkable advantages
ing a single-frame image cannot provide time-varying
over deterministic approaches. The advantage of the stacharacteristics of the moving target. Therefore, it is nectistical framework is its flexibility. In this way, the foressary to develop temporal SAR GMTIm based on the
mulation could model a particular structure in a
statistical sparsity-based framework, which is a promisprobabilistic way and also allows for a fitting of the
ing research direction in SAR GMTIm technology. In
likelihood.
fact, Sandia Laboratory has successfully realized Video■ The utilization of uncertainty information during
SAR GMTIm, where the processed results have been
parameter estimation is important for a performance
released on their official website. In particular, the
gain. Particularly, in conventional approaches, the error
100

IEEE SIgnal ProcESSIng MagazInE

November 2016

Table of Contents for the Digital Edition of Signal Processing - November 2016