IEEE Geoscience and Remote Sensing Magazine - December 2021 - 183

null (target absent) and alternative (target present) hypotheses,
respectively, and data independence across the multiple
views is assumed. By comparing the likelihood ratio with a
threshold c determined using the Neyman-Pearson theorem
[77], a fused binary image Ff
can be defined as
Fi j (, ) = (
f
1
if
if
LR ij
LR ij
( ,)
( ,)
2
#
c
c
(6)
.
The second method applied the LRT detector to individual
images, followed by fusion of the detected binary
images through a pixel-by-pixel multiplication. Since the
clutter generates different image-domain signatures when
observed from different viewpoints, both strategies take
advantage of the clutter diversity provided by the multiple
views, though the latter scheme does not require the data
independence assumption across the multiple views.
An adaptive version of the LRT detector of [53] was proposed
in [78] to allow enhanced multiview detection of lowsignature
targets in a rough surface clutter environment. To
achieve a more accurate estimation of the image-domain
statistics, the target and clutter distributions were iteratively
adjusted by means of a two-step procedure. The first
step aimed at separating the image into target and clutter
regions, whereas the second step used the extracted target
and clutter regions to update the target and clutter statistics.
This process was repeated until convergence was achieved.
-275
A binary image from [78], corresponding to the image presented
in Figure 4, is reported in Figure 12. In [78], it was
shown that an adaptive detector can outperform its nonadaptive
counterpart in terms of the false-alarm rates while
providing comparable detection performance.
A robust LRT detector, under the independence viewpoints
assumption, was proposed in [79] for multiview FLGPR
imaging. Instead of modeling the distributions of the
target and clutter pixels with parametric families, a band
of feasible probability densities under each hypothesis was
constructed using training data. The detector was then designed
such that it minimized the maximum error probability
for all feasible density pairs within the two bands.
This relaxed the strong assumptions about the clutter and
noise distributions, rendering the detector robust against
statistical model deviations. The minimax approach is critical
in cases where accurate estimation of the distribution of
the background clutter may be challenging.
A binary image from [79], corresponding to the image of
Figure 4, is depicted in Figure 13. It was demonstrated that,
5
4
3
2
1
-280
-1
-2
-3
-4
-5
012345678 910111213141516
x (m)
-285
-10
-5 05
Along Array (m)
(a)
-216
-214
-212
-210
-208
-206
-10
-5 05
Along Array (m)
(b)
10
10
FIGURE 12. The detection result for the image presented in Figure 4
obtained through the adaptive procedure [78]. The red areas indicate
the detected target regions, while the black areas represent
false alarms. (Source: [78].)
5
3
1
4
2
-1
-3
-5
FIGURE 11. An FL-GPR-processed image in [76]. The × symbol indicates
false alarms, + indicates fiducial alarm, and a circle indicates
a target. The panels correspond to two different regions along a
track that have slightly different lengths: (a) -285 to -275 m and
(b) -216 to -206 m. (Source: [76].)
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
1
7
3
02468 10 12 14 16
x (m)
FIGURE 13. The detection result for the image presented in Figure 4
obtained using the robust LRT detector. (Source: [79].)
183
5
6
9
8
Along Track (m)
Along Track (m)
y (m)
y (m)
IEEE Geoscience and Remote Sensing Magazine - December 2021

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