IEEE Geoscience and Remote Sensing Magazine - June 2021 - 22

the principle of the CA method is introduced using a dualbaseline
(DB) InSAR system for the sake of simplicity. The
absolute phases of the two interferograms with different
normal baseline lengths can be defined by
Bs ks Bs ks2221 11 22
+= +
ks i 12
i
=
ks2
·( () () )·(()()),{{rr (15)
where ()(, ) is the integer ambiguity of the sth
pixel of interferogram i. If we transform (15) into a linear
equation with ()
()
regarded as the dependent variable and
ks1
as the independent variable, we have
() ·( )
ks B
B
2 =+ B1
1
1
2
ks
{{
r
Bs Bs
2
21() - 12()
.
Bs Bs B2{{ r 1
21
-
ks ks
12
12
(16)
The slope of (16) is a constant (i.e., BB /21), so all of the
pixels with the same ambiguity vector (i.e., [( ), ()]) will
share the same intercept, i.e., (()()).
By using the pattern on the intercept, the histogram-based
CA method is used to group the pixels into different clusters
(the details on the histogram method can be found in
[62]). After the clustering analysis process, the intercept
value I(l) of the lth cluster center can be obtained, i.e.,
() (()()).
Il Bl Bl B2{{ r 1
formed into
21 12
kl B
B
kl i 12
i
=
2 () ·()( ),=+ (17)
1
2
kl Il
1
where ()(, ) is the ambiguity number of the lth
cluster's center. Under this condition, the solution to (17),
i.e., [( ), ()],
kl kl
12
can be calculated according to some special
combination of a normal baseline length based on the
CRT [4], [62]. Then, the absolute phase of each pixel that
belongs to the corresponding cluster can be directly obtained
(all of the pixels in the same cluster share the same
ambiguity vector). For example, Figure 13(a) (the normal
baseline length is 370.45 m) and Figure 13(b) (the normal
baseline length is 130.62 m) are two real-filtered interferograms
(single pass) generated by the TanDEM-X DB data
set. Figure 13(c) is the intercept image of Figure 13(a) and
(b), which shows that all of the pixels in a fringe share the
same ambiguity vector.
Recently, research on how to improve the robustness
of CA has attracted great interest as in the literature. Liu
et al. put forward a CA-based, noise-robust PU method
using a density-based clustering algorithm [63]. In addition,
a refined CA algorithm employing the new interferograms
after the linear combination was presented
in [64] to further improve noise robustness. Yuan et al.
proposed a novel CA-based MB PU and filtering method
[65] that combines the closed-form solving formulas
of the cluster-ambiguity vector phase-filtering strategy
with the optimal baseline to increase the robustness of
the traditional CA method. Compared with the traditional
CRT-based MB PU, the two main advantages of
the CA method are that 1) the CA method can eliminate
the nonexistent ambiguity vectors in the actual terrain
with the assistance of the histograms, which increases
PU robustness, and 2) the PU procedure can be operated
cluster by cluster, which relies only on the information
of the cluster centers so that the execution time can
be reduced.
=- Then, (16) can be transMB
PU METHODS USING DEEP LEARNING
Although the aforementioned CA method has several attractive
possibilities, it still has the main disadvantage
that, when the fringes of the interferogram change violently
due to steep terrain or are polluted by strong phase
noise, the intercept clusters will not be well distinguished
so that the histogram method cannot accurately find all
of the clusters. To solve this problem, Zhou et al. [66] proposed
an unsupervised DCNN to cluster all of the pixels
into different groups according to the input-recognizable
pattern on the ambiguity number of the MB-interferometric
phase, which is an extension and an improvement
of the traditional CA method using a deep learning
technique (the CANet). In this framework, an extended
pattern space, including an intercept and interferometric
fringe (that is, the intercept-fringe pattern), was proposed
to feed into CANet, which provides the robust distinguishability
for CANet.
Figure 13(d) shows the intercept-fringe pattern of
Figure 13(a)-(c). Then, CANet with a deep architecture
is devised to extract the detailed features from an
-2
2
-2
2
(a)
(b)
(c)
0.5
-0.5
(d)
FIGURE 13. (a) A real interferogram with long normal baseline. (b) A real interferogram with a short normal baseline. (c) The intercept image
of (a) and (b). (d) The intercept-fringe pattern of (a), (b), and (c) [66].
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IEEE Geoscience and Remote Sensing Magazine - June 2021

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