IEEE Geoscience and Remote Sensing Magazine - March 2020 - 50

The DIn phase can be further expressed as
z = z 1 - z 2 = -

4r(R - Rl )
+ (z obj1 - z obj2). (18)
m

Assuming that the scattering characteristics of the target remain unchanged during imaging, the phase contains only
the difference of propagation:

z=-

4r(R - Rl )
4rTR
=, (19)
m
m

where k is an integer that indicates ambiguity, z def represents the deformation phase component, z atm represents
the atmospheric phase component, and z noise represents
the error phase component, such as system thermal noise
that can be filtered out by interferometry phase filtering.
Figure 12 shows these phase components schematically [1].
When the target area deforms considerably, the DIn phase
may exceed one phase period (22r), which means that z
will be entangled within the interval (-r, r).

where z depends mainly on the propagation difference TR
between the phase center of the antenna and the ground
target. When affected by factors such as the atmospheric
delay and various phase noises during electromagnetic
wave propagation, z may also contain these components,
which can be modeled as [54]

INTERFEROMETRY PHASE FILTERING
From (20), the DIn phase of the GB-DInSAR usually contains many other phase components that may seriously affect its deformation-inversion accuracy. The filtering process of the thermal noise phase z noise is called phase filtering,
which is an important part of DIn.
A summary of four classical and efficient interferometr
y phase-filtering algorithms, including Goldstein

z = z def + z atm + z noise + 2kr, (20)
adaptive filtering based on correlation coefficients, gradient-based
adaptive filtering, circular-periodic
mean filtering, and weighted cirImages
cular-period median filtering, are
...
1
2
3
N-1
N
N+1
given in [55]. Goldstein filtering is
Consecutive
a classical InSAR filtering algorithm
Interferogram
that removes noise in the frequency
Single
domain [56]. The gradient-based
Reference
adaptive filtering algorithm calculates the weight coefficient of the
Multibaseline
center data of the filtering window
according to the gradient of the 2D
signal: the larger the signal gradient, the smaller the weight coeffiFIGURE 11. A DIn combination in GB-DInSAR [1].
cient. Then, the weighted average of
the elements in the window replaces the data at the center of the window. The algorithm improves mean
Phase Images φ1
DIn Phase φ
filtering. By judging the signal graφ2
Phase (φ)
dient, the data with large gradients
are weighted slightly, and the edge
0
2π
of the interferometry fringe is weakened. Accordingly, the edge detail
information of the interferometry
fringes is effectively preserved [57].
φatm
φnoise
Periodic mean filtering assumes
φdef
that the interferometry phase value
itself is sampled relatively slowly.
The filtering is performed using the
statistical local mean of the interferometry phase. Weighted circularperiod median filtering combines
the advantages of circular-period
mean filtering and those of circularAtmospheric
Deformation
Error Phase
Phase Component
Phase Component
Component
period median filtering to simultaneously filter Gaussian and particle
noises [58].
FIGURE 12. The phase components of the DIn phase [1].
50

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

MARCH 2020

IEEE Geoscience and Remote Sensing Magazine - March 2020

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