IEEE Geoscience and Remote Sensing Magazine - December 2021 - 184

compared to detectors based on parametric models, robust
detectors can lead to significantly reduced false-alarm rates,
particularly in cases where there is a mismatch between the
assumed model and true distributions. Both the robust and
parametric detectors were extended to incorporate statistical
dependence between multiview images via a copulabased
function in [80].
SPECTRAL APPROACHES
To improve the detection performance of plastic objects, a
time-frequency approach was proposed in [30]. The detection
problem was conventionally formulated by considering
a signal corrupted by interference. To deal with the nonstationary
nature of both the signal and clutter, the authors
employed time-frequency distribution to provide temporal
localization of the signal spectral components. The detector
considered the signal time-frequency representation based
on the Choi-Williams distribution or, equivalently, the
ambiguity function and applied discriminant features extracted
using principal component analysis plus the linear
discriminant method [81], [82]. The effectiveness of this approach
and the employed detector was demonstrated using
experimental results.
Frequency subband processing was used in [83], together
with co- and cross-polarized signals, for enhanced target-detection
performance in FL-GPR sensing. Images were
formed using one wide subband and four narrow-frequency
subbands within a 2.5-GHz signal bandwidth to analyze
the frequency dependency of landmines and clutter. An FLGPR
image, corresponding to the copolarized (VV) signal
over multiple subbands, is shown in Figure 14. It is evident
that the clutter is particularly strong, but its distribution
changes over the frequency bands considered. On this basis,
a number of features, including the magnitude, local
contrast, ratio between copolarized and cross-polarized
signals, and features of polarimetric decompositions, were
extracted at each narrow-frequency subband and employed
to assess their role in target detection. For this purpose, the
authors considered a Fisher's linear discriminant (FLD)based
classifier, which can be mathematically described as
follows. With C1
and C2 representing the " false-alarm " and
" target " classes, respectively, and given N training feature
vectors {, ,, }nN1
xn
= f
that have been labeled as C1
that maximizes the class separation as
() ,
ym mSw21
=FLD
m
i 12i
=
-1
is the within-class scatter matrix, defined as
()()
()() .
N
Sx1
wn
C
=- -
+- -
: /
x !C2
n
n
xn ! 1
n
n
mx m T
11
22
/ xm xm T
D
(8)
When an unlabeled testing data point is collected, its confidence
value is determined by the projection of its feature
vector on
C ,2 FLD finds the projection direction in the feature space
(7)
where ,, , is the mean feature vector of the ith class
and Sw
and
y ,FLD and it is classified by means of simple
thresholding.
In [84], the authors performed target detection using
space-wavenumber processing and a feature-based
method, employing data measured by means of a vehiclemounted
FL-GPR equipped with a MIMO array. The approach
was applied in the image domain and relied on the
definition of a bistatic scattering function associated with
selected pixels. A set of images achieved with different incident
and scattering angles was used to estimate the bistatic
scattering function. Experimental results demonstrated
that the proposed method can offer an efficient feature vector
for landmine discrimination.
An original approach to process measured data collected
at the U.S. Army test site using the radar system
24
20
16
12
8
-4 04 -4 04 -4 04 -4 04 -4 04
Cross-Track
Range (m)
(a)
Cross-Track
Range (m)
(b)
Cross-Track
Range (m)
(c)
Cross-Track
Range (m)
(d)
Cross-Track
Range (m)
(e)
FIGURE 14. An example of images achieved with the FL-GPR system in [83] keeping unchanged the illuminated scene and polarization (VV)
but exploiting different frequency subbands: (a) 0.8-2.8, (b) 0.75-1.35, (c) 1.25-1.85, (d) 1.75-2.35, and (e) 2.25-2.85 GHz. The black circle
indicates the true target location. (Source: [83].)
184
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE DECEMBER 2021
Along-Track Range (m)
Vehicle Direction
IEEE Geoscience and Remote Sensing Magazine - December 2021

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2021
