IEEE Geoscience and Remote Sensing Magazine - June 2020 - 75

where W uI z denotes the pixel of W I z at site u, and T is the
threshold. The estimation of W uI x is refined during the second step, using Wiener filtering as
max d

u Iux h2 - v 2W
^W
n uu
u uI x h2 , 0 $ W I x,
^W

(33)

where v 2W is the noise variance in the wavelet domain.
Therefore, InSAR BM3D filters possess the superiorities of
the NL and wavelet-domain filters. In addition to the wavelet-domain filter, other advanced methods have been proposed, such as pyramidal representation [87], higher-order
SVD [24], and so on [88]-[92].

REVIEW OF NEWLY ADVANCED METHODS
With the development of new signal processing concepts,
such as sparse signal processing and machine/deep learning [93], [94], advanced methods have been proposed for
InSAR phase denoising. Among them, sparse methods
[95], [96] have drawn a lot of attention and shown potential. There is a high probability that these methods will
make good candidates for the next generation of InSAR
phase denoising.
The sparse methods can retrieve a noise-free image by
applying a sparse constraint in a generalized formulation as
min is i0,
x/s, W

EXPERIMENTAL ANALYSIS
As an example of a typical method, the NL-InSAR algorithm proposed in [21] is applied to illustrate NL-filter
performance. First, experiments are performed using the
aforementioned data; the filtered images appear in Figure 11. The search-window size is 15 # 15 pixels, the patch
size is 5 # 5 pixels, and h = 12. As Figure 11 shows, the NLInSAR filter deals well with the smooth area that has little
disturbance; however, there are filtered-phase artifacts in
the high-heterogeneity and highly slopped areas. More experiments are implemented using the RADARSAT-2 repeatpass interferometric sample data. Due to the resolution
limitation, the search window size is 11 # 11 pixels, the
patch size is 3 # 3 pixels, and h = 6. Figure 12 presents the
filtered images and shows that NL-InSAR is very powerful
for phase and amplitude denoising in areas with buildings.

3
2
1
0

3
2
1
0

-1

-1

-2
-3

-2
-3

(a)

subject to )

x = M ^z 1, z 2 h
s = W ^ x h,

(34)

where < $ < 0 is the L 0- norm of a vector; x/s is the noisefree image to be recovered, containing the actual phase
z x; W is a dictionary or operator to sparsely represent x, z 1;
and z 2 are the vectors of the interferometric pair of SAR
images z 1 and z 2, respectively. In (34), x = M ^z 1, z 2 h is
a linear or nonlinear function derived by mapping z 1
and z 2 to x, which can be treated as a uniform formulation of (9), (10), and (11). Accordingly, sparse technology
can perform noise reduction on the real phase, complex
phase, and interferogram, respectively. The direct solution
of (34) is very difficult to calculate because it is a nondeterministic-polynomial time-hard problem. Solving (34)
also depends on the forms of M and W. In the following,
two typical groups of sparse methods are discussed, considering their contributions.

0.8
0.6

(b)

0.4
0.2
(c)

(d)

0

FIGURE 11. The filtered phase images obtained using the NL-InSAR filter [21] (Mount Etna data). The (a) filtered phase, (b) phase difference,
(c) residues, and (d) coherence of the filtered images.

3
2
1
0

3
2
1
0

3
2
1
0

-1

-1

-1

-2
-3

-2
-3

-2
-3

(a)

(b)

(c)

(d)

FIGURE 12. The filtered images obtained using the NL-InSAR filter [21] (RADARSAT-2 data). The (a) original phase, (b) filtered phase,

(c) phase difference, and (d) filtered amplitude.
JUNE 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

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IEEE Geoscience and Remote Sensing Magazine - June 2020

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