Signal Processing - November 2016 - 96

2
1.5

10
Range Cell

Angle (rad)

1
0.5
0
-0.5

20
30

-1

40

-1.5
-2

0

10

20
30
Pulse Number
(a)

40

50

50

Range Cell

Range Cell

10
15
20
Cross-Range Cell
(b)

25

10

20
30
40
Cross-Range Cell

50

10

10
20
30

20
30

40
50

5

40

10

20
30
40
Cross-Range Cell

50

50

(c)

(d)

FIGURE 7. The radar imaging with 25 pulses (50% of the full measurements and SNR = 20 dB): (a) random phase error, (b) RDA method, (c) a method in [47]
(without uncertainty information) (NMSE X = - 4.0294 dB, MSE { = 0.4019), (d) a method in [47] (with uncertainty information) (NMSE X = - 12.4399 dB,
MSE { = 0.0059 ).

information to achieve higher estimation accuracy and
Autofocus meets structured sparsity
therefore a better-recovered radar image. This work is also
The basic idea in [47] is to iteratively estimate the sparse
validated using the Yak-42 data. As observed in Figure 8(a),
scatterer coefficients and the phase error to jointly induce
directly applying the RDA method can
sparsity. However, the objective of radar
barely lead to a concentrated image. In
imaging is to obtain the most concentratThe statistical treatment
Figure 8(b), the image obtained by , 1-mined radar image rather than the sparsest
of the sparsity-based
one. Therefore, a merely sparsity-inducing
imization presents a reasonable profile of
algorithm can properly
scheme may result in undesirable image
the airplane. However, it is still blurred,
utilize uncertainty
results, because it considers only sparsity
and some of the true scatterers are not
information during
as the performance measure. More prerecovered correctly. In contrast, the methiterations to improve the
cisely, a simple sparsity constraint cannot
od in [47] obtains a better-concentrated
sufficiently preserve the weak scatterers
image and removes most of the undesirestimation accuracy.
or reduce background noise to a desirable
able artifacts, as seen in Figure 8(c). With
quality. A possible solution to obtain a more concentrated
these comparisons, we conclude that the proper utilization
radar image rather than a mere sparse one is to exploit
of uncertainty information substantially enhances the perstructured sparsity. In [49], the sparse Bayesian model is
formance in autofocus applications.
sophisticatedly modified to exploit structural sparsity. More
The statistical treatment of the sparsity-based algorithm
specifically, the spatial consistency along range cells is
can properly utilize uncertainty information during iterations
exploited, and therefore the framework can cope simultaneto improve the estimation accuracy. In fact, we have demonously with structured sparse signal recovery and phase error
strated how this uncertainty information can be properly used
correction in an integrated manner. The focused high-resothroughout this particular application. Compared with the reglution radar image can be obtained by iteratively estimating
ularized approach, statistical sparsity-based algorithms do not
the sparse scatterer coefficients and phase errors to jointly
require the time-consuming parameter tuning for improved
obtain a structured sparse solution.
performance as those in the , 1-regularized cases.
96

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November 2016

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