IEEE Geoscience and Remote Sensing Magazine - March 2019 - 46

3
2

100

1
0

50

-1
-2

0

-3
(a)

(b)
Altimetry Ground Truth
L1 Norm
L2 Norm

100

50

Deformation (cm)

200
150

Good Pixels

Good Pixels

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50
0

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(c)

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Pixels
(d)

FIGURE 7. (a) The ALOS PALSAR differential interferogram. (b) The PU result of the L2 norm. (c) The PU result of the L1 norm. (d) Deforma-

tion profiles on the altimetry track.

of the Advanced Land Observing Satellite (ALOS) PALSAR, in
which the noisy area is mostly an open water area [52]. Because September corresponds to Congo River's low-waterlevel season and December to high-water-level season [53],
the absolute phase of Figure 7(a) can provide the water-level change between September and December. Figure 7(b)
and (c) are the PU results obtained by the L2 -norm method
and the L1 -norm method, respectively.
In this experiment, the measurement obtained by radar altimetry is used as the ground truth. Although radar
altimetry is initially designed to determine the ocean
surface topography, recent research indicates that it also
has an accuracy advantage for measuring the water level
of wetlands or floodplains [54]-[56]. The line in Figure  7(a) is the Envisat altimeter track. An altimeter is a
profiling tool, not an imaging tool, so the Envisat altimeter can obtain the water level only along its track. The estimated water level change from Envisat data is shown in
Figure 7(d). Without a ground control point in this area,
InSAR can provide only the relative deformation information between neighboring pixels, so there should be
an offset between altimetry-derived and InSAR-derived
water level changes.
Ideally, the profile of water level change in Figure 7(a)
should be parallel with that of altimetry. If we avoid the
46

noisy area (i.e., open water area), the standard deviation of
the difference in water level changes obtained from altimetry and the L1 norm on the left range of high-quality pixels is 10.7 cm, and that of the difference between altimetry
and the L2 -norm results on the left range of the high-quality pixels is 13.7 cm. In addition, the standard deviation of
the difference between altimetry and the L1 -norm results
on the right range of the high-quality pixels is 11 cm, and
that of the difference between altimetry and the L2 -norm
results on the right range of the high-quality pixels is
12.3 cm. The range of the high-quality pixels is marked in
black on the line in Figure 7(a).
Comparing the Envisat altimetry measurements, we can
see that the L1 -norm result agrees better with the altimetry-derived water level change than does the L2 norm,
although the PU result of the L2 norm is smoother than
that of the L1 norm. However, it should be noted that we
cannot absolutely conclude that the Lp norm is totally useless when p 2 1. As examples, [57] used the PU result of the
L2 norm to design a phase-noise-filtering algorithm, and
[24] designed a PU method with an extra adaptive filtering
function by means of combining the L1 and L3 norms. In
addition, unlike most other optimization-based methods,
the L2 -norm PU method has an advantage in terms of execution time [6], [58]-[61].
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