IEEE Geoscience and Remote Sensing Magazine - March 2020 - 127

B 2({ 1(s) + 2k 1(s)r) = B 1({ 2(s) + 2k 2(s)r), (9)

where B i (i = 1, 2) is the perpendicular baseline of the ith
interferogram; { i(s) (i = 1, 2) is the flattened, wrapped interferometric phase of the sth pixel in the ith interferogram;
and k i(s) (i = 1, 2) is the ambiguity number of the sth pixel
in the ith interferogram. It should be noted that in (9) k 1(s)
and k 2(s) are integers. Under this condition, the Chinese remainder theorem [53] offers a unique solution to (9) with
a special combination of normal baselines [53]. Thus, (9)
does not need any assumption or constraint condition, and
MB PU becomes a well-posed problem, not the ill-posed one
prevalent in traditional 2D PU. For more details about the
MB PU technique, readers are referred to [35] and [54]-[58].
Yu et al. [53] initially tested the MB PU method across
wetlands. The study used three PALSAR images obtained
on 19 June, 19 September, and 20 December 2007 to generate two differential interferograms across the Congo wetlands, as shown in Figure 5(a) and (e). The details of the
two interferograms are summarized in Table 1. Figure 5(e)
shows a higher number of fringes because it was generated
using SAR images from the low- and high-water seasons,
while Figure 5(a) was generated through SAR images from
the low-water seasons [59].
The second and the third columns in Figure 5 correspond
to the unwrapped phase using the SB MCF PU method and
the MB InSAR PU methodology-based terrain-deformationestimation approach (MTDA) [53], respectively. A significant
difference between the two methods can be observed in the
black-box region in Figure 5(b), which displays a linear unreasonable phase jump. On the other hand, Figure 5(c), derived
using the MTDA, presents a smooth unwrapped phase. Figure 5(d) is the water-level-change map generated by subtracting the unwrapped phase of one interferogram from another
unwrapped phase through the SB PU method [Figure 5(b) and
(f)]. Figure 5(h) is the water-level-change map generated from
the unwrapped phase using the MTDA [Figure 5(c) and (g)].
Figure 6(a) compares the water-level-change profiles
between Envisat radar altimetry, three-pass DInSAR, and
the MTDA. The standard deviation of the differences between the red-circle line and blue-triangle line is 28.19 cm,
and that of the black dotted line and blue-triangle line is
25.32 cm, which suggests that the estimated water-level
change obtained by MB PU agrees better with the altimetryderived water-level changes.
Figure 6(b) reveals the water-level changes extracted
along the arbitrarily chosen white line in Figure 5(d)
and  (h). It can be seen that there is a clear water-levelchange jump in the traditional 2D PU result, which is likely
an artifact. Conversely, the water-level change obtained
by MB PU is continuous and smooth. Overall, the waterlevel change from MB PU [Figure 5(h)] is more accurate
and credible than that of SB PU [Figure 5(d)] since the MB
PU method does not need to obey the phase-continuity
MARCH 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

LARGE SCALE OF WETLANDS
Some riverine and coastal wetland systems are vast. For example, the Congo and Amazon wetland areas are estimated
to be 2.27 # 10 5 [60] and 8.4 # 10 5 km 2 [61], respectively.
The Louisiana coastal wetlands cover an area of roughly
20,000 km 2, extending 300 km of the coastline [62]. This
large scale presents a challenge to understanding 2h/2t
continuity across whole wetlands through InSAR from one
path. Yuan et al. [13] mosaicked interferograms from seven
ALOS paths to map the middle reach of the Congo wetlands,
whereas Cabrera and Wdowinski [62] mosaicked interferograms from two Radarsat-1 and seven ALOS paths to map

250
Water-Level Change (cm)

	

assumption. In summary, the PU procedure's performance
directly determines the quality of the final InSAR-derived
water-level changes in wetlands. Hence, to successfully obtain a credible PU result, more research about advanced
methodologies must be conducted.

Altimetry Ground Truth
Traditional Three-Pass DlnSAR
MTDA
Good
Good
Pixels
Pixels

200
150
100
50
0
-50
0

20

40
60
Pixels
(a)

80

Traditional Three-Pass DlnSAR
MTDA

0
Water-Level Change (cm)

InSAR is shown in (9) (readers can straightforwardly extend
to the MB case) [53]:

-10
-20
-30
-40
-50
0

200

400
600
Pixels
(b)

800

FIGURE 6. (a) A profile comparison of the water-level changes

between Envisat radar altimetry, three-pass DInSAR, and the MTDA
method. The location of the profile is referenced to the line in
Fig-ure 5(a) and (e). (b) The profile comparison of the water-level
changes between three-pass DInSAR and the MTDA method. The
location of the profile is referenced to the line in Figure 5(d) and (h).
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IEEE Geoscience and Remote Sensing Magazine - March 2020

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