Signal Processing - November 2016 - 97

Due to the utilization of the structured sparse constraint,
the proposed method preserves the target region and alleviates the overshrinkage problem, as compared to the previously presented sparsity-driven autofocus approaches.
The superior performance of the structured sparsity-based
technique is shown in Figure 9. Compared with other
approaches, the structured sparsity-based autofocus method
achieves a better-concentrated image, with more coefficients recovered in the target region with different undersampling ratios.

120

Range Cell

100

60
40
20

Statistical sparsity-based SAR GMTIm
Imaging ground moving targets in SAR has become
increasingly important. Conventionally, in imaging a
potentially moving target, hypotheses of the target
motion were constructed to match the signal by a filter
bank [50]. In the scenario of closely located targets, however, their responses cannot be well distinguished from
each other. Recent advances in sparsity-based SAR
GMTIm [5], [16], suggest that sparsity can be properly
exploited to enable multitarget processing and higher
accuracy. This application is rather different from the
previously introduced ones, since the received radar
echoes can no longer be simply modeled as a sum of harmonics but rather as multicomponent LFM signals with
unknown chirp rates. Therefore, the key challenge in
SAR GMTIm is to properly formulate a mathematical
model that allows a sparse representation of the images
for moving targets. In [16], the signal model was constructed as a sparse linear model, where an overcomplete
dictionary was constructed by using a discretized velocity
grid. Although empirical results demonstrate the success
of the method, its performance is inhibited by the discretization errors in the dictionary. In this section, we briefly
review two recent works based on statistical sparsity from
different angles.
In [51], a statistical framework was formulated to obtain
the moving target image, which could avoid the construction of a large overcomplete dictionary. In particular, this
work considers a K channel SAR system with F passes,
collecting data from P azimuth angles and Q range cells.
The complex-valued raw SAR image is decomposed as [51]
Y p, f = E p, f . (L p, f + S p, f + N p, f ),
p = 1, ..., P and f = 1, ..., F,
Q#K

(17)

where Y p, f ! C
denotes the raw SAR image at azimuth p
and pass f, E p, f ! C Q # K is the corresponding spatial-temporal calibration error, L p, f ! C Q # K represents background
clut ter, S p, f ! C Q # K models t he moving t a rget, a nd
N p, f ! C Q # K models the noise. Since the number of parameters to be estimated is much larger than the number of observations Y, proper priors must be selected for each of these
parameters. Interested readers are referred to [51] for more
details. Here, we only highlight the key statistical models in
this formulation.

50
40
30
20
Cross-Range Cell
(a)

40
60
80
100
Cross-Range Cell
(b)

120

40
60
80
100
Cross-Range Cell
(c)

120

Range Cell

100
80
60
40
20

120

Range Cell

100
80
60
40
20

FIGURE 8. The radar imagery results with one-half of the measurements,
obtained by (a) RDA, (b) a method in [14], and (c) a method in [47].

■

IEEE SIgnal ProcESSIng MagazInE

The clutter L p, f is decomposed into a sum of a passinvariant background term B p and a pass-specific
speckle term X p, f . Assuming that the background clutter B p can be represented by one of several classes,
such as a road or buildings, a complex Gaussian prior is
used for B p with a set of unknown covariance matrices
that account for different classes, where each covariance matrix follows an inverse Wishart distribution.

November 2016

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