IEEE Geoscience and Remote Sensing Magazine - March 2020 - 126

Wrapped
Interferogram

SB
Unwrapped Interferogram
3
2
1
0
-1
-2
-3

(a)

(b)
3

30
20
10
0
-10
-20
-30

(c)

1
0
-1
-2
-3

(f)

Deformation Map
30
20
10
0
-10
-20
-30

50
0
-50
(d)

30
20
10
0
-10
-20
-30

30
20
10
0
-10
-20
-30

2

(e)

MB
Unwrapped Interferogram

(g)

60
40
20
0
-20
-40
-60
(h)

FIGURE 5. (a) The wrapped interferogram with a long perpendicular baseline. The straight line shows the track of the Envisat radar altimeter. (b) The unwrapped phase of (a) obtained by the L1- norm SB PU method. (c) The unwrapped phase of (a) using the MTDA. (d) The deformation map between (b) and (f), in centimeters. (e) The wrapped interferogram with a short perpendicular baseline. (f) The unwrapped
phase of (e) obtained by the L1- norm SB PU method. (g) The unwrapped phase of (e) using the MTDA. (h) The deformation map between
(c) and (g), in centimeters.

To correctly unwrap the fringe pattern shown in Figure 4(b), it is necessary to make the PU integration path climb
the hill (that is, in the direction of the increasing interferometric phases) so that the PU method builds the branch cuts
that join the residues in "clumps" rather than pairs. However,
traditional single-baseline (SB) PU algorithms (except the
L0- norm PU strategy [49], [50]) build dipole cuts between
each pair of residues. Thus, the traditional PU method [such
as the minimum cost flow (MCF) method, also called the L1norm PU strategy] cannot generate continuous, smooth unwrapped phases across these wetlands [35], [51]. Although
the L0- norm PU strategy may provide the desired result for
this kind of fringe, Chen and Zebker [52] demonstrated that
the L0- norm PU problem is a nondeterministic polynomialtime hard one, meaning that an exact solution cannot be obtained by any method in polynomial time.
One approach is to use the mask cut to assist the PU
across the wetlands. Taking Figure 4(b), which is a segment

TABLE 1. THE DETAILS OF THE INTERFEROGRAMS ILLUSTRATED
IN FIGURE 5(a) AND (e).

INTERFEROGRAM

SAR IMAGES

WATER
SEASON

PERPENDICULAR
BASELINE (M)

Figure 5(a)

19 June-
19 September 2007

Low-
Low

99.3

Figure 5(e)

19 September-
20 December 2007

Low-
High

39.39

126

of Figure 4(a), as an example, it can be seen that the phase
gradient in the wetlands is generally parallel to the riverflow direction and the phase jumps are clear at the borders
between the unflooded upland and flooded wetlands [48].
The direct application of traditional PU methods can produce discontinuities in the unwrapped phase, as shown in
Figure 4(c). The discontinuities are caused by the inappropriate formation of the branch-cuts that connect the residues.
To avoid such artifact discontinuities, the wetlands can be
divided into segments according to the channels. Then, each
segmented wetland area can be extracted from the original interferogram over which the traditional PU can be applied. Finally, all of the segmented wetlands are mosaicked
by adding an offset value to the adjacent wetlands, based
on the assumption that the adjacent wetlands have phase
differences lower than r, as shown in Figure 4(d). However, this method should be used cautiously, especially for
wetlands separated by levees because they can have distinct
water-level-change patterns [20].
Besides the mask-cut technique, the multibaseline (MB)
PU is an innovative technique for application across wetlands. Unlike traditional 2D PU, MB PU does not need to
obey the phase-continuity assumption. Therefore, MB PU
can be applied to the complicated discontinued interferometric phase. This is because the baseline diversity enables
MB PU to significantly enhance the interferometric phase's
ambiguity intervals. Thus, MB PU completely eliminates
the phase-continuity assumption. Taking the dual-baseline
(DB) case as an example, the fundamental principle of DB
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

MARCH 2020
IEEE Geoscience and Remote Sensing Magazine - March 2020

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