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remote sensing

Article

Improving CPT-InSAR Algorithm with Adaptive Coherent

Distributed Pixels Selection

Longkai Dong 1,2,3 , Chao Wang 1,2,3,* , Yixian Tang 1,2,3, Hong Zhang 1,2,3 and Lu Xu 1,2,3

Citation: Dong, L.; Wang, C.; Tang,

Y.; Zhang, H.; Xu, L. Improving

CPT-InSAR Algorithm with Adaptive

Coherent Distributed Pixels Selection.

Remote Sens. 2021,13, 4784. https://

doi.org/10.3390/rs13234784

Academic Editor: Zhong Lu

Received: 9 October 2021

Accepted: 22 November 2021

Published: 25 November 2021

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1Key Laboratory of Digital Earth Science, Aerospace Information Research Institute, Chinese Academy of

Sciences, Beijing 100094, China; donglk@aircas.ac.cn (L.D.); yxtang@radi.ac.cn (Y.T.);

zhanghong@radi.ac.cn (H.Z.); xulu@radi.ac.cn (L.X.)

2International Research Center of Big Data for Sustainable Development Goals, Beijing 100094, China

3University of Chinese Academy of Sciences, Beijing 100049, China

*Correspondence: wangchao@radi.ac.cn; Tel.: +86-10-82178161

Abstract:

The Coherent Pixels Technique Interferometry Synthetic Aperture Radar (CPT-InSAR)

method of inverting surface deformation parameters by using high-quality measuring points pos-

sesses the ﬂaw inducing sparse measuring points in non-urban areas. In this paper, we propose the

Adaptive Coherent Distributed Pixel InSAR (ACDP-InSAR) method, which is an adaptive method

used to extract Distributed Scattering Pixel (DSP) based on statistically homogeneous pixel (SHP)

cluster tests and improves the phase quality of DSP through phase optimization, which cooperates

with Coherent Pixel (CP) for the retrieval of ground surface deformation parameters. For a region

with sparse CPs, DSPs and its SHPs are detected by double-layer windows in two steps, i.e., mul-

tilook windows and spatial ﬁltering windows, respectively. After counting the pixel number of

maximum SHP cluster (MSHPC) in the multilook window based on the Anderson–Darling (AD)

test and ﬁltering out unsuitable pixels, the candidate DSPs are selected. For the ﬁltering window,

the SHPs of MSHPC’ pixels within the new window, which is different compared with multilook

windows, were detected, and the SHPs of DSPs were obtained, which were used for coherent estima-

tion. In phase-linking, the results of Eigen decomposition-based Maximum likelihood estimator of

Interferometric phase (EMI) results are used as the initial values of the phase triangle algorithm (PTA)

for the purpose of phase estimation (hereafter called as PTA-EMI). The DSPs and estimated phase are

then combined with CPs in order to retrievesurface deformation parameters. The method was vali-

dated by two cases. The results show that the density of measuring points increased approximately

6–10 times compared with CPT-InSAR, and the quality of the interferometric phase signiﬁcantly

improved after phase optimization. It was demonstrated that the method is effective in increasing

measuring point density and improving phase quality, which increases signiﬁcantly the detectability

of the low coherence region. Compared with the Distributed Scatterer InSAR (DS-InSAR) technique,

ACDP-InSAR possesses faster processing speed at the cost of resolution loss, which is crucial for

Earth surface movement monitoring at large spatial scales.

Keywords:

interferometric synthetic aperture radar (InSAR); statistically homogeneous pixels (SHPs);

distributed scattering pixel (DSP); phase-linking (PL); deformation

1. Introduction

Interferometry synthetic aperture radar (InSAR) has been widely used in Earth surface

movement monitoring [

1

–

9

]. In the past 20 years, the rapid development of multi-temporal

InSAR (MT-InSAR) has effectively suppressed the problems of spatial-temporal deco-

herence [

10

] and atmospheric phase delay of the differential interferometric synthetic

aperture radar (D-InSAR) technique [

11

]. The permanent scatterer InSAR (PS-InSAR) tech-

nique

[12–14]

is used to process permanent scattering targets with a high signal-to-noise

ratio, and it is widely used in surface deformation monitoring at the original spatial resolu-

Remote Sens. 2021,13, 4784. https://doi.org/10.3390/rs13234784 https://www.mdpi.com/journal/remotesensing

Remote Sens. 2021,13, 4784 2 of 19

tion. The Small Baseline Subset (SBAS) InSAR technique [

15

] suppresses the spatiotemporal

decoherence problem by selecting interferometric pairs with short spatiotemporal baselines.

The coherent pixels technique InSAR (CPT-InSAR) [

16

–

18

], which combines the ad-

vantages of PS-InSAR and SBAS-InSAR, was proposed in order to reduce the errors caused

by the small number of images and to improve the accuracy of estimation parameters. CPT-

InSAR is also able to retrieve linear and nonlinear components of movement from a set of

low resolution interferograms, estimating DEM errors and atmospheric artifacts at the same

time, and it is widely used in surface deformation monitoring [

19

–

21

]. However, when the

selected coherence threshold is high, CPT cannot select a sufﬁcient number of points in the

low coherence region, which will cause observation points to be disconnect [

22

]. When the

selected coherence threshold is low, the points with low phase quality could be selected as

the measuring points, deteriorating the accuracy of the inversed parameter [

12

]. In order to

improve measuring point density and monitoring accuracy of CPT, phase quality should

be improved along with the low coherence region, where they are not selected as coherent

pixels. Currently, there is no method for increasing the measuring point density of the

CPT-InSAR method.

The PS-InSAR technique usually selects PS points with relatively stable scattering

characteristics in time and strong echo signals as observation objects, and PS includes

artiﬁcial buildings, lighthouses, exposed rocks and artiﬁcially deployed corner reﬂectors.

Similarly to CPT-InSAR, it is difﬁcult to obtain enough measurement points in non-urban

areas with low coherence. In order to tackle this problem, various methods have been

proposed for increasing the density of measuring points, such as Stable Point Interferometry

over Unurbanised Areas (SPINUA) [

23

], Persistent Scatterer Pair InSAR (PSP-InSAR) [

24

]

and Cousin PSs InSAR (CSP-InSAR) [

25

]. Additionally, fusion algorithms were proposed

in order to properly combine PS and distributed scatterer (DS) to increase the density

of measurement points [

26

–

28

]. Ferretti A. et al. introduced new approaches in 2011,

SqueeSAR [

29

], in order to jointly process PS and DS, taking into account their different

statistical behaviors. SqueeSAR takes DS points as PS candidate points for space adaptive

ﬁltering and phase linking, which greatly increases the density of measuring points, and

it is considered second-generation PS-InSAR technology. Most methods for increasing

the density of measuring point are suitable for single-look processing, and there is no

systematic method for CPT-InSAR multilook processing.

The SqueenSAR method and its derived DS-InSAR method processing framework

are processed in the single look, and the processing of homogeneous pixel detection and

phase linking in DS-InSAR method is very time consuming and only practically applicable

for ground surface deformation monitoring in small areas [

30

,

31

]. In 2014 and 2017, the

European Space Agency (ESA) launched Sentinel-1A and Sentinel-1B satellites with a revisit

period of 6 days, and its coverage width of wide scan mode is 250 km and is open to

global users, which indicates that SAR technology enters into the era of Big Data [

32

]. It is

obvious that traditional DS-InSAR technology is not applicable in the processes of regularly

monitoring large spatial scale deformations. The processing idea of improving the density of

monitoring points in SqueeSAR is a good method. We learn from the processing framework

and ideas of SqueenSAR and propose a method suitable for CPT multilook processing.

The identiﬁcation of statistically homogeneous pixels (SHPs) and phase optimization

of DS includes two key steps in the DS-InSAR technique. The Kolmogorov–Smirnov (KS)

test [

29

,

33

], Anderson–Darling (AD) test [

34

,

35

], Kullback–Leibler scatter test (KL) [

36

,

37

]

and Cramervon Mises (CM) test [

38

] are nonparametric tests that have been used for

the identiﬁcation of SHPs. Mi Jiang et al. proposed a fast SHPs method (FaSHPS) to

extract homogeneous points, which signiﬁcantly improves the speed of homogeneous

pixels detection [

39

]. Compared with other test methods, the AD statistic is powerful for

detecting changes in the shape parameter and changes within a scale family [

35

]. Methods

of estimating the phase sequence from all possible interferograms fall under phase linking

(PL) [

30

]. The difference between PL and SBAS lies in the full and partial utilization of

interferogram abundance [

40

]. In 2011, Ferretti et al. proposed PTA in order to optimize the

Remote Sens. 2021,13, 4784 3 of 19

DS target phase, resulting in a new direction of MT-InSAR [

29

]. Since then, several methods

for phase optimization were proposed, e.g., phase-decomposition-based persistent scatterer

InSAR (PD-PS InSAR) [

41

], component extraction and selection SAR (CAESAR) [

42

], Eigen

decomposition-based Maximum-likelihood-estimator of Interferometric phase (EMI) [

30

]

and sequential estimator [

31

]. Multipolarization data were also used in DS target detection

and phase optimization [43].

In order to overcome the limitation that the CPT-InSAR method only selects high-quality

coherence scatterers that result in low density of measuring points in non-urban and low

coherence areas, we propose a new method called ACDP-InSAR, which can adaptively

extract and process urban and non-urban measuring points by combining CPs with DSPs,

simultaneously improving the density of measuring points under multilook processing

based on the DS-InSAR processing flow. The conventional DS-InSAR method improves

the density of monitoring points in single-look data, while ACDP-InSAR designs a set of

processing flow in multilook suitable for CPT-InSAR. For low coherent regions that are

not selected for CPs, DSPs and its SHPs are obtained through a double-layer window. For

the first layer of multilook windows, the maximum statistically homogeneous pixel cluster

(MSHPC) within the window needs to be detected, and if the pixel number of clusters is

greater than a certain threshold, the window is considered as a candidate DSP. For the second

layer of the filter window, the SHPs of each pixel in the MSHPC within the window were

detected. By integrating homogeneous pixels, the SHP of the DSP is obtained. In order to

obtain the optimal phase for each time period, the coherence matrix is processed by using

the PTA-EMI method. The DSP and its optimized phase are subsequently processed together

with CPs in order to achieve the purpose of increasing the density of measuring points.

2. Methodology

2.1. CPT-InSAR Method

When generating an interferogram by conjugate multiplication of two SAR images, its

phase variation between neighboring pixels be expressed as follows [16]:

δφint =δφﬂat +δφtopo +δφmov +δφatm +δφnoise (1)

where

δφﬂat

is the ﬂat earth component related to the range distance;

δφtopo

is the topo-

graphic phase;

δφmov

is the component due to the displacement of the terrain in the range

direction (line of sight (LOS)) between both SAR acquisitions;

δφatm

is the phase related to

atmospheric artifacts; and

δφnoise

comprises degradation factors related with temporal and

spatial decorrelation and thermal noise. With respect to this,

δφmov

has two contributions,

linear and nonlinear displacement, described as follows:

δφmov =δφlinear +δφnonlinear =4π

λ·∆v·T+δφnonlinear (2)

where

λ

is the wavelength;

∆v

includes the velocity increments between neighboring

pixels; and T is the temporal baseline between both SAR acquisitions. Not all points satisfy

the linear model, and points with high phase quality need to be selected for the solution.

The CPT-InSAR method generates an average coherence map by estimating the average

coherence of all points in the multilook window from the entire interferogram stack, and

then it sets a threshold to select points with high coherence quality as candidate CPs. Then,

all the neighboring pixels of irregularly gridded data generating nonoverlapped triangles

are related by the Delaunay triangulation method. The linear components of movement

and DEM errors are estimated by maximizing the following model coherence function:

γ(xm,ym,xn,yn)

=1

N

N

∑

i=0

exp[j·(δφdif(xm,ym,xn,yn,Ti)

−δφmodel(xm,ym,xn,yn,Ti))]|

(3)

Remote Sens. 2021,13, 4784 4 of 19

where Nis the number of interferograms,

δφdif

is the differential phase increment and

δφmodel

is the phase increment of the theoretical linear model. According to the coherence

threshold of the triangulation edge, the connection with low quality is rejected. The CPT

method used an approach based on the classical region growing algorithm for phase

unwrapping [

43

]. The integration [

44

] starts from different seed points, which are chosen

from those presenting links with better model coherences, and calculates the absolute value

of velocity for each pixel by using the following equation.

vestimated(x,y)

=

∑

i

[vestimated(xi,yj)+∆vestimated(x,y,xi,yj)]·γmodel (x,y,xi,yj)

∑

i

γmodel (x,y,xi,yj)

(4)

Subsequently, the linear deformation rates and elevation errors at each measuring

point solved by integration are then used to calculate the nonlinear components of ground

surface deformation and atmospheric artifacts.

2.2. SHPCs Detection for DSP

Since the mathematical expectation of radar signals is not attainable in practice, under

the assumption of distributed targets, coherence is usually estimated by spatially averaging

radar echoes in a moving window [45]:

ˆ

γ=

L

∑

i=1

s1i

∗

s2i·ejφ(i)

sL

∑

i=1

|s1i|2sL

∑

i=1

|s2i|2

(5)

where idenotes the i-th pixel in a coherence-estimate window (CEW), s

1

and s

2

are complex

signals from coregistered InSAR images and

∗

is a complex conjugate operator. For

each CEW, Lpixels are used to obtain a coherence estimate.

ˆ

γ

is the estimated value of

window coherence. The averaging in this method does not consider the homogeneity of

neighboring pixels.

Backscattering amplitude statistics are a suitable method for adaptively grouping

and averaging pixels in order to preserve the phase signatures of natural structures in

the observed area [

29

]. The AD statistic is powerful at detecting changes in the shape

parameter and detecting changes within a scale family [

32

]. In this paper, the AD test

method is used to identify homogeneous pixels based on multitemporal amplitude data:

A2

M,M=M

2∑

X∈{XP,i,Xq,i}

(ˆ

Fp(X)−ˆ

Fq(X))2

ˆ

Fpq(X)(1−ˆ

Fpq(X)) (6)

where

ˆ

Fpq(X)

is the empirical cumulative distribution functions of the pooled distribution

obtained by combining the two independent datasets,

Xp

,

i

and

Xq

,

i

,

i=

1,

. . .

,

M

, into

dataset

X=Xp,i,Xq,i

. The AD test method is used to test each pixel within a multilook

window in order to obtain the MSHPC within the multilook window, and the schematic

diagram of AD test in multilook window is shown in Figure 1. The pixel number of MSHPC

is used to determine whether the window is considered as a candidate DSP, and the steps

for selecting a candidate DSP are as follows.

(1) In the multilook windows (size is N*M), for image pixel F(pixel x

i

, pixel y

j

), by

applying the two-sample AD test to amplitude data vectors, other pixels within the window

that are considered statistically homogeneous with pixel F are selected given a certain level

of signiﬁcance.

(2) The image pixels in a multilook window that, although selected by the AD test, are

not connected to P directly or through other SHPs are discarded.

Remote Sens. 2021,13, 4784 5 of 19

(3) Repeat steps (1) and (2) for the pixels within the

windowM

(

windowM

is a multilook

window), respectively, where i= 1, 2, 3

. . .

N and j= 1, 2, 3

. . .

M until all pixels in all

windows are detected, and the homogeneous cluster

Ω=[Ω1,Ω2,Ω3. . . . ΩN×M]

of each

individual pixel is obtained.

(4) Judging the pixel number of MSHPC in each cluster, the window for which its

pixel number of MSHPC is greater than a certain threshold is the candidate DSP (and the

MSHPC are Ωmax).

Figure 1.

Process of MSHPC acquisition. After testing all pixels in the window, the SHPCs, which

have the maximum pixel number of SHPs, include MSHPC.

The above is the method of the candidate DSPs selection. We consider the pixel as

a candidate DSP when the pixel number of MSHPC in the multilook window is greater

than the threshold. As shown in Figure 2, the yellow pixels in the red box region are the

SHPs of the MSHPC in the multilook window. It is worth mentioning that not only the AD

test method could be used in testing but also various methods for testing homogeneous

pixels can be used for testing. The phase quality of candidate DSP is poor compared to

the high coherence region. In order to improve the phase quality of DSP, spatial ﬁltering

is performed based on homogeneous pixels after determining DSP with reference to the

spatial ﬁltering technique of SqueenSAR. The steps of homogeneous pixel identiﬁcation

for SHPΩmax are as follows.

Figure 2.

Example of the double-layer hypothesis testing window. The red window is the multilook

window, the yellow pixels are the SHPs of the multilook window and the green window is the spatial

ﬁltering window of a single SHP.

(1) The second homogeneous pixel test was performed for each SHP in

Ωmax

, and

the window size was winA

×

winR. By using pixel P

max

(P

max∈Ωmax

) as the central pixel,

Remote Sens. 2021,13, 4784 6 of 19

the intensity vectors of pixel P

max

and other pixels q (q

∈windowF

,

windowF

as the ﬁlter

window) in the ﬁlter window are tested by using the AD test method to identify SHPs

with Pmax.

(2) The image pixels in the ﬁlter window that, though selected by the AD test, are not

connected to Pmax directly nor through other SHPs are discarded.

The

SHPΩmax

of DSP and

SHPﬁlter

of each

SHPΩmax

are selected to prepare coherent

estimations for improving the target phase’s quality. Once the proper estimation window

has been deﬁned for each image pixel, by carefully selecting SHP families, amplitude data

can be despeckled, interferometric phase values can be ﬁltered and coherence values can

be estimated properly.

2.3. The Phase Optimization of DSPs

It should be noted that the same

SHPﬁlter

will exist in different

SHPΩmax

. In the phase

estimation, in order to avoid the duplication of the same pixel, the

SHPﬁlter

of different

SHPΩmax

should be integrated, and the duplicate

SHPcoherence

should be removed to obtain

the ﬁnal

SHPcoherence

for coherent estimation. After identiﬁcation of the

SHPcoherence

, it is

possible to estimate the sample covariance matrix given by the following:

C(W) = Ehd(W)d(W)Hi≈1

|ΩC|∑

P∈ΩC

d(P)d(P)H=ˆ

C(7)

where H indicates Hermitian conjugation, and

ΩC

is the set of

SHPcoherence

used in the

sample estimate of the covariance matrix.

d(P)=[d1(P), d2(P), . . . dN(P)]H

is the complex

data vector of generic image pixel, and

di(P)

is the complex reﬂectivity value of the i-th

image of the data-stack corresponding to pixel P.

d(W)=[d(P)1,d(P)2, . . . d(P)NC]

is

the complex data vector of the

SHPcoherence

used to estimate coherence, and NC is the

pixel number of

SHPcoherence

. The covariance matrix

ˆ

C

is an N

×

N Hermitian positive

semideﬁnite matrix, with N being the number of SAR images. For phase optimization,

suppose that the coherence matrix of multilook windows can be expressed as follows [

29

].

Γ(W)=ΘYΘH(8)

Y is an N ×N symmetric real-value matrix for which its elements correspond to the

coherence values of all the interferograms.

Θ

is an N

×

N diagonal matrix containing the

values of the “true” phase values of multilook-windows W, related to the optical path of

the radar beam in each acquisition. The probability distribution function of the SHP can be

expressed as follows [46]:

W(dΩ|θ)∝∏

p∈Ω

exp−dH

PΘY−1ΘHdp=h−traceΘY−1ΘHˆ

Γi (9)

where

θ=[θ1,θ2, . . . , θN]T

is simply the vector of the phase values of N available images in

correspondence to the multilook windows. The estimated result

θ

of maximum likelihood

(ML) is obtained by maximizing this probability distribution function or minimizing the

absolute value of its logarithm [

47

,

48

]. The optimal estimate of the N phase values is then

given by the following.

ˆ

θ=argmax

θexp[−trace(Φγ−1ΦHˆ

Γ(W))]

=argmax

θexp[−ΛH(γ−1◦ˆ

Γ(W))Λ]

=argmax

θΛH(γ−1◦ˆ

Γ(W))Λ

(10)

Φ

is an N

×

N diagonal matrix,

Φ=diag{exp(iθ)}

;

Λ

is an N-dimensional vector,

Φ=exp(iθ)

and

◦

represents the Hadamard product. Therefore, it is necessary to use an

iterative method to ﬁnd the parameters corresponding to the minimization of

Equation (9)

Remote Sens. 2021,13, 4784 7 of 19

in order to obtain the optimal phase sequence. However, iterative computation using the

BFGS method is extremely time consuming [

46

]. If an initial value close to the optimal

solution is provided, it will greatly increase the speed of iteration.

The EMI method differs from the PTA method by introducing additional degrees of

freedom for the estimation in maximizing the Wishart likelihood distribution [

49

], turning

the problem into a biobjective optimization problem. In order to improve computational

efﬁciency, the EMI method reduces the optimization problem to a maximum eigenvector

problem by solving the following equation.

ˆ

Γ(W)−1◦Cˆ

θinitial =λˆ

θinitial (11)

This is the formulation of eigen decomposition of the Hadamard product

ˆ

Γ−1◦C

,

with

λ

as the minimum eigenvalue and

ˆ

θinitial

as its corresponding eigenvector. We use

the phase sequence

ˆ

θinitial

solved by the EMI method as the initial value for the solution

of

Equation (9)

in order to speed up phase optimization and to enhance the speed of the

solution while ensuring the accuracy of the solution. We refer to this method as PTA-

EMI. After the optimal phase has been estimated, the phase estimation results need to be

evaluated. We evaluate the results by using the temporal coherence estimation method

used in the PTA algorithm [29,50].

γ=2

N2−NRe

N

∑

n=1

N

∑

k=n+1

eiφnk e−i(ϑn−ϑk)(12)

2.4. The Process of ACDP-InSAR

We have described the processing chain of the CPT algorithm, the SHP used to identify

the DSP coherence estimate based on the AD algorithm and the optimization of the DSP

phase by using the PTA-EMI algorithm. After the coregistration image is processed by the

above method, the standard CPT-InSAR processing chain can be used to reproduce the

parameters of CPs and DSPs. The ﬂow chart of ACDP-InSAR is shown in Figure 3and can

be described as follows.

(1) The time baseline and the space baseline are used to select the appropriate com-

bination of the interference. The average coherence of the interferometric combination

is calculated with an N

×

M window, and the CPs are selected by setting the coherence

threshold.

(2) The operations of preprocessing the magnitude images of N images and then

ﬁnding the non-CP region and sparse-CP region SHPs based on the method outlined in

Section 2.2 are conducted to determine the DSP target and to record the SHP used to

estimate the DSP’s coherence matrix.

(3) The estimation of the coherence matrix of the DSP target using SHP and of the

optimal phase sequence based on the PTA-EMI is performed as described in Section 2.3.

(4) Based on the phase triangularity and the optimized phase, the phase dataset of

DSP under the above interference combination is calculated.

(5) The phase information of CP and DSP are jointly processed according to the CPT

processing work chain in order to invert the physical parameters of the measuring point.

The N phase sequences estimated using the PTA-EMI method have the following

phase triangularity:

φij =θj−θi(13)

where

φij

represents the phase difference between time points iand j;

θj

and

θi

represent

the phase values between time points iand j. In coherence estimation, complex data are

used, and topographic phases should be removed [

51

]. Compared with the traditional

CPT method, the ACDP-InSAR method does not develop a hybrid processing chain but

retrieves homogeneous pixels in the low coherence region based on the AD test method in

Remote Sens. 2021,13, 4784 8 of 19

order to obtain the coherence matrix and uses the PTA-EMI method to obtain the optimal

phase value for jointly processing CPs and DSPs.

Figure 3. Algorithm ﬂow chart of ACDP-InSAR.

3. Experiment

3.1. Case 1: Mountainous Areas in Southwestern China

3.1.1. Study Area and Dataset

The proposed method is validated by 31 descending Sentinel-1 SAR images acquired

from 12 October 2018 to 19 October 2019 over mountainous areas in the southern region of

Bijie city, Guizhou Province, China (see Figure 4a). Due to rough terrain and vegetation

in the area, it is difﬁcult for the conventional CTP-InSAR algorithm. Sentinel-1 SAR is

C-band, with its wavelength of 5.6 cm. The nominal resolutions in azimuth and slant-range

directions are 5 and 20 m, respectively, corresponding to pixel dimensions of 2.3 and 13.9 m.

The SAR image of the study area contains 1600

×

8000 pixels, covering approximately

21 km ×21 km

in the azimuth and range directions. Figure 4b shows the TanDEM-X 90 m

Digital Elevation Model (DEM) downloaded from the German Aerospace Center (DLR)

EOC GEOSERVICE data portal. As observed from Figure 4d, the study area mainly in-

cludes impervious, evergreen broadleaved forest, shrubland, evergreen shrubland, rainfed

cropland, water bodies and buildings. The results of land use classiﬁcation are obtained

from the Data Sharing and Service Portal supported by the Big Earth Data Science Engineer-

ing Program (http://data.casearth.cn/sdo/detail/5d904b7a0887164a5c7fbfa0, accessed on

9 October 2021) [52], and the classiﬁcation information is shown in Table 1.

Remote Sens. 2021,13, 4784 9 of 19

Figure 4.

(

a

) The location of Sentinel-1 data in China, and the black box represents range of Sentinel-1. (

b

) Geographic

location of the coverage of the SAR acquisitions superposed on the TanDEM, and the blue box represents the range of

Sentinel-1 data. (c) The optical image of study area, and (d) is the classiﬁcation result of land used in the study area.

Table 1. Classiﬁcation Information of Figure 4d.

Number Classiﬁcation System Color

1 Impervious (195,20,0)

2 Evergreen broadleaved forest (0,100,0)

3 Shrubland (150,100,0)

4 Evergreen shrubland (150,75,0)

5 Rainfed cropland (255,255,100)

6 Closed deciduous broadleaved forest (170,200,0)

7 Irrigated cropland (170,240,240)

8 Water body (0,70,200)

3.1.2. Data Processing and Result

We use TanDEM and precise orbit data to preprocess Sentinel-1 data and then gener-

ated the single look complex (SLC) data after coregistration. The date of the main image

used in the registration is 12 October 2018, and the amplitude image of the main image is

shown in Figure 5a. We follow the steps in Section 2.4 in order to process SLC data. When

calculating the average coherence coefﬁcient, the coherence of the interference pairs within

a certain baseline threshold and spatial threshold is averaged. The multilook ratio between

the azimuth and range is 4:20. The average coherence coefﬁcient of the study area is shown

in Figure 5b. According to statistics, the average coherence coefﬁcient of the entire study

area is 0.165. When selecting CPs, the coherence threshold is 0.5; that is, the pixels with

the average coherence coefﬁcient greater than 0.5 are selected as CPs. The results of the

traditional CPs selection method with a coherent threshold at 0.5, 0.375 and 0.25 are shown

in Figure 5c,d,e, respectively. In Figure 5c,d and Figure 5e, there are 329, 808 and 1872

coherent pixels, respectively. Although the number of CPs with low threshold is obviously

more than the number of CPs with high threshold, the poor phase quality of CPs with

low coherence threshold will affect the accuracy of deformation results. Therefore, the

coherence threshold of CPs used in this experimental area is 0.5 for deformation inversion.

By comparing the spatial relationship between the magnitude map, optical image, land

Remote Sens. 2021,13, 4784 10 of 19

used data and CP, it was observed that CPs are mainly distributed in the built-up areas of

the township and on bare rock. It should be noted that the coordinate system in Figure 5is

the SAR coordinate system, while the optical image coordinate system in Figure 4is the

WGS-84 coordinate system.

Figure 5.

(

a

) Magnitude image of the master image where the date is 20181012. (

b

) Average coherence

coefﬁcient of an interference pair. (

c

) CPs’ spatial distribution with a coherent threshold as 0.5. (

d

) CPs’

spatial distribution with a coherent threshold as 0.375. (

e

) CPs’ spatial distribution with a coherent

threshold as 0.25. (

f

) DSPs’ spatial distribution. The white pixel (value as 1) represents the measuring

point of CPs and DSPs in (c–f).

DSP is extracted by using the method outlined in Section 2.2. First, the amplitude

dataset is corrected, and the amplitude value is normalized. The multilook window in the

DSP selection is 4:20, and the threshold value of the maximum pixel number of clusters

is selected as 48; that is, the window with the maximum pixel number of MSHPC greater

than 48 is selected as the candidate DSP. The dimensions of the window used to identify

SHPΩmax

is about four hectares, which corresponds in pixels to a window of 21

×

21. By

considering the testing time and the distribution of homogeneous statistical areas, this

detection range is reasonable in non-urban areas. The threshold of SHP rejection is 20 in

ﬁlter window. By ﬁxing 20 as the minimum number of SHP on which spatial ﬁltering can

be carried out, it is possible to preserve information of highly coherent targets [

29

]. Finally,

the candidate DSPs were judged based on the pixel number of SHPs: The candidate DSPs

Remote Sens. 2021,13, 4784 11 of 19

below 48 were rejected, and the remaining candidate DSPs are the ﬁnal DSPs. The results

of DSP pixel selection are shown in Figure 5f, with 4499 measuring points. By comparing

the spatial relationships of the magnitude map, optical images and DSP, it was found that

DSP points were mainly distributed in agricultural ﬁelds and submerged vegetation areas.

In the experimental area, the number of DSPs was approximately 10 times of the number

of CPs with the coherent threshold as 0.5. It should be noted that the effect of monitoring

point density enhancement is more related to both topography and geomorphology, and

the effect has a better performance in non-urban areas.

In order to show the validity of the PTA-EMI method, we processed data not only

possessing DSP but also all pixels. After using PTA-EMI, we acquired N ﬁltered differential

interferograms. These N differential interferograms are the optimized phase after spatial

ﬁltering and temporal ﬁltering. We selected three interference phases before and after

ﬁltering for comparison, as shown in Figure 6. It can be observed that the quality of the

interference phase obtained by the proposed method has been greatly improved, which

proves the effectiveness of the algorithm. Figure 7shows the results of temporal coherence

calculated according to Equation (11), which takes values in the range of 0–1, with larger

values representing better temporal coherence and better temporal phase estimation results.

It can be observed from the Figure 7that the temporal coherence of the county and low

vegetation is better, while the temporal coherence of the broadleaf forest is worse.

Figure 6.

(

a

–

c

) are the original phases of interference pairs 20191007–20191019, 20190913–20191019

and 20190209–20190317, respectively. (

d−f

) Phases 20191007–20191019, 20190913–20191019 and

20190209–20190317 after ACDP-InSAR processing.

Remote Sens. 2021,13, 4784 12 of 19

Figure 7. Time coherence of the study area in mountainous areas.

After optimizing the phase of the DSP pixels, we fuse the CPs and their phase with the

DSP pixels and its phase, and the merged pixels are named mixed coherent pixels (MCPs).

The phase of the CPs is the original phase and has not been processed by phase optimization.

According to the CPT method, the Delauney triangulation [

53

] of MCPs is constructed

and enters the phase, slope distance, incident angle and baseline parameters into the

triangulation. Finally, the deformation rate of the MCPs is obtained through integration.

The results of the deformation rate based on the CPT method and the deformation rate

based on the ACDP-InSAR method in the study area of case 1 are shown in Figure 8. By

comparing the two results, it can be observed that the number of measuring points has

increased signiﬁcantly, and the results of the deformation rate are more consistent, which

proves the effectiveness and reliability of the algorithm proposed in this paper.

Figure 8.

(

a

) The surface deformation rate of the study area obtained by the CPT method. (

b

) The surface deformation rate

of the study area obtained by the method proposed in this paper.

3.2. Case 2: Shigatse M5.9 earthquake in Tibet, China

3.2.1. Study Area and Dataset

The proposed method is validated by 29 descending Sentinel-1 SAR images acquired

from 10 January 2020 to 21 December 2020 over the middle Himalayan Mountains (see

Figure 9c). The SAR image of the study area contains 2000

×

14000 pixels, covering

approximately 31 km

×

27 km in the azimuth and range directions. Figure 9a shows the

TanDEM-X 90m DEM of the study area, and Figure 9b shows the Sentinel-2 optical images

of the study area. The study area is located at the junction of the Indian plate and the

Eurasian plate in the Himalayan seismic zone. According to the website of the China

Earthquake Networks Center, an earthquake of magnitude 5.9 occurred in Tingri County,

Shigatse City, Tibet, on 20 March 2020, and the focal depth was 10.0 km. There have been

Remote Sens. 2021,13, 4784 13 of 19

134 earthquakes of magnitude three and above within 200 kilometers of the epicenter in

the past 9 years. The largest earthquake was a magnitude 7.5 earthquake that occurred in

Nepal on 12 May 2015.

Figure 9.

(

a

) The location of Sentinel-1 data in China, and the black box represents range of Sentinel-1.

(

b

) Geographic location of the coverage of the SAR acquisitions superposed on the TanDEM, and the

blue box represents the range of Sentinel-1 data. (

c

) Optical image of the study area of Shigatse M5.9

earthquake in Tibet, China.

3.2.2. Data Processing and Result

The date of the main image used in the coregistration is 8 January 2020, and the

amplitude image of the main image is shown in Figure 10a. We follow the steps in

Section 2.4

to process the SLC data of the study area in case 2. The multilook ratio between

azimuth and range is 4:20. The ground features in this area are mainly grassland and bare

rock, with high coherence. Therefore, in order to monitor points with exceptional quality,

the coherence threshold is set to 0.6.

Figure 10. (a) Magnitude image of the master image 20200108. (b) Average coherence coefﬁcient of the interference pair.

Remote Sens. 2021,13, 4784 14 of 19

DSP is extracted by the method outlined in Section 2.2. The amplitude dataset is

corrected after coregistration, and the amplitude value is normalized. Then, the multilook

window in the DSP selection is 4:20, and the threshold value of the maximum pixel number

of cluster is 48. Then, the homogeneous pixels of the

SHPΩmax

were tested, and the other

parameters were the same as those in case 1. The coherence matrix is estimated by SHP,

and the phase of DSPs is optimized by the PTA-EMI method. Case 1 has proven that the

effect of phase optimization is obvious, and it is no longer veriﬁed in this experiment.

The results of the deformation rate based on the CPT method and the deformation

rate based on the ACDP-InSAR method in the Shigatse M5.9 earthquake are shown in

Figure 11.

By comparing both results, it can be observed that the number of measuring

point has increased signiﬁcantly, and the results of the deformation rate are more consistent.

The measuring point number of CPs is 14516 and the measuring point number of CPs and

DSPs is 95462. The increase in the density of monitoring points allows detecting surface

deformations more clearly. It can be observed from Figure 11 that the fault zone of the

earthquake is very obvious, and the range and absolute value of surface subsidence on the

east side are larger than the range and absolute value of surface uplift on the west side.

There is no monitoring point in the center of the deformation ﬁeld because the deformation

gradient is too large, which results in decoherence. From the phase of the interference pair

20200320–20200427, the maximum deformation can be roughly calculated to reach 300 mm.

The study area is a medium-high coherence area, but the conventional CPT-InSAR cannot

meet the demand for measuring point density for seismic deformation inversion.

Figure 11.

(

a

) The surface deformation rate of the study area in case 2 obtained by the CPT-In- SAR method. (

b

) The surface

deformation rate of the study area in case 2 obtained by the method proposed in this paper.

4. Discussion

It can be observed from the experimental results that the method proposed in this

paper will increase the density of monitoring points and improve phase quality. When

detecting SHPs in a double-layer window, the size of the window can be dynamically

adjusted. The size of the multilook window depends on the multilook number of the

average coherence coefﬁcient, which should be uniﬁed; otherwise, CP and DSP cannot be

combined. The size of the ﬁltering window will affect the ﬁlter’s result. A small window

will render the ﬁlter unapparent, but a window that is too large induce computational

burden and may lose details. In some scenes, the ﬁlter window is too large to retrieve more

SHPs, which is an invalid operation. Therefore, the corresponding window size should

be set according to different application scenarios. In order ensure the homogeneity of

multilook windows, a large threshold should be used.

In the era of SAR Big Data, the processing efﬁciency of algorithms is the basis of big

data processing. The PTA-EML method used in this paper has improved efﬁciency over

PTA phase optimization. It should be noted that the algorithm for identifying MSHPC

is too redundant when extracting DSPs. The mutuality of hypothesis testing can be used

Remote Sens. 2021,13, 4784 15 of 19

to enhance the speed of the MSHPC test. Mutuality of AD test means that the test result

between data group B and data group A when A as main body is the same as the test

result when B as the main body. It is not necessary to examine each pixel when retrieving

MSHPC in multilook windows, because the SHPCs of pixel A and the SHPC of A’s SHP are

practically the same. Therefore, it is only necessary to classify the pixels in the window by

their statistical characteristics, and the cluster with the largest pixel number is the MSHPC

of this window.

Phase optimization is a more time-consuming step [

37

], and the pixel number of DSPs

selected by ACDP-InSAR in mulitilook scenes is much smaller than the pixel number of DS

points selected by SqueenSAR in the single-look scenes. Therefore, the processing speed of

the proposed method is faster than that of the conventional SqueenSAR algorithm. Taking

case 1 as an example, we counted the time consumed by ACDP-InSAR and SqueenSAR

in SHP selection and phase-link steps. The statistical diagram of algorithm running time

is shown in Figure 12. The diagram shows, in Figure 12, that the processing speed of

ACDP-InSAR in SHP selection is lower than that of SqueenSAR, and the processing speed

of the phase link is higher than that of SqueenSAR. The overall processing speed of the

method proposed in this paper signiﬁcantly improved. On the other hand, the proposed

method has a cost of resolution reduction. The ACDP-InSAR method is more suitable for

high precision surface deformation monitoring in large spatial scales.

Figure 12.

Cumulative processing time of the ACDP-InSAR and SqueenSAR over case 1 as an

assessment of computational efﬁciency.

In Section 3, we used two experiments to prove effectiveness in non-urban areas,

which has a good effect of increasing the number of points. Unfortunately, no in situ

measurement data could be applied to quantitatively verify the accuracy of the algorithm

in t experiment areas. In order to quantitatively evaluate the algorithm accuracy proposed

in this paper, the measurement data for Beijing, China, was used. The ﬁeld observation

points covering 40 different regions in Beijing, China, from 2017 to 2018 were collected.

However, the measurement period of the measured leveling data is one year, which cannot

be compared with the InSAR results in a long time series. We changed the leveling data

into annual average settlement and compared it with the annual average deformation rate

of ACDP-InSAR. Before comparison, the vertical deformation of leveling data was changed

into the deformation along the LOS direction according to satellite parameters. The area of

accuracy veriﬁcation and data comparison between leveling data and ACDP-InSAR result

are shown in Figures 13 and 14, respectively.

As observed from Figure 13c, the leveling results are practically consistent with the

results of ACDP-InSAR, and individual ﬁeld observation points are different. The speciﬁc

data values are compared, as shown in Figure 14. According to statistics, the root mean

square error (RMSE) between ACDP-InSAR results and leveling data is 5.45 mm/year,

which proves that ACDP-InSAR results are reliable.

Remote Sens. 2021,13, 4784 16 of 19

Figure 13.

The experimental area for ACDP-InSAR accuracy veriﬁcation. (

a

) The location of the

experimental area, and blue box represents the range of leveling data. (

b

) Distribution map of ﬁeld

observation points. Each benchmark in the ﬁgure has a corresponding label, and the color of each

ﬁeld observation point represents the annual average deformation rate obtain from leveling data.

The corresponding color label is same as the color label in (

c

). The result of overlaying the level data

deformation rate above the ACDP-InSAR deformation rate.

Figure 14.

Comparison between in situ leveling measurements and InSAR results estimated by the

proposed method over the ﬁeld observation points in Figure 13b.

The ACDP-InSAR method not only has the advantages of the CPT-InSAR method

but also has better density with respect to measuring points and detectability than those

of the latter method. Of course, the ACDP-InSAR method also has some limitations.

Firstly, ACDP-InSAR is an improvement of the CPT-InSAR method, which estimates

coherent values by multilook processing; thus, it will degrade resolution. Low resolution

Remote Sens. 2021,13, 4784 17 of 19

is not suitable for ﬁne deformation measurement, such as deformation monitoring of

dams, bridges and regional buildings. Secondly, both the ACDP-InSAR method and the

CPT-InSAR method solve the results by constructing a network. In large spatial scale

deformation monitoring, the process of removing edges with low coherence and causing a

set of CPs to be divided into several clusters is easy. Future investigations should establish

a multi-layer network to connect multiple clusters during large spatial scale data processing

in order to ensure the consistency of regional deformation monitoring.

5. Conclusions

In this paper, we proposed method ACDP-InSAR method in order to improve measur-

ing point density based on distributed scattering targets for solving the problem of sparse

measurement points in non-urban areas caused by CPT-InSAR. ACDP-InSAR identiﬁes

SHPs with two-layer windows based on the AD test. The ﬁrst multilook window selects

the DSP, and the second ﬁlter window determines the SHPCs of the DSP. The CP target is

selected on the coherence coefﬁcient map after multilooking, while the DSP needs to be

selected under the single-look scene. Therefore, the resolution of DSP should be consistent

with that of CP. The SHP of DSP is used to estimate the coherence matrix of DSP, the PTA-

EMI method is then used to optimize phase sequences, and a set of optimal phase sequence

with phase triangularity is obtained. We selected two regions as experimental areas located

in the mountainous region of Southwest China and around Shigatse on the Tibet Plateau.

The experimental results show that the density of monitoring points increases approx-

imately 5–10 times, and the phase quality is improved, verifying the effectiveness and

applicability of the algorithm. The ACDP-InSAR method can not only acquire monitoring

points in a low-coherence region but also increase the density of monitoring points in a

medium-coherence region. The root mean square error (RMSE) between ACDP-InSAR

results and leveling data is 5.45 mm/y, which proves that ACDP-InSAR results are reliable.

Compared with the conventional DS-InSAR technology, this method improves processing

speed at the cost of resolution loss and is suitable for Earth surface movement monitoring

in large spatial scales.

Author Contributions:

Conceptualization, L.D., C.W. and H.Z.; methodology, L.D. and Y.T.; software,

L.D. and Y.T.; validation, L.D., C.W. and L.X.; formal analysis, L.D. and H.Z.; investigation, L.D.;

resources, C.W., H.Z., L.X. and Y.T.; data curation, L.D.; writing—original draft preparation, L.D. and

L.X.; writing—review and editing, C.W., H.Z. and Y.T.; visualization, L.D. and L.X.; supervision, C.W.

and H.Z.; project administration, C.W.; funding acquisition, C.W. All authors have read and agreed

to the published version of the manuscript.

Funding:

This research was funded by the Strategic Priority Research Program of the Chinese

Academy of Sciences, Grant No. XDA19090126, and the National Natural Science Foundation of

China, Grant No. 41930110.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement:

Sentinel-1 data were provided by the European Space Agency (ESA)

and are available from the Alaska Satellite Facility (ASF) (https://vertex.daac.asf.alaska.edu, accessed

on 9 October 2021). TanDEM-X 90m DEM data are available at https://download.geoservice.dlr.de/

TDM90, accessed on 9 October 2021.

Acknowledgments:

The authors would like to thank ESA and EU Copernicus Program for providing

Sentinel-1A SAR data and DLR for providing TanDEM-X 90m DEM data. Bo Zhang, Fan Wu, Wei

Duan and Jing Wang of Aerospace Information Research Institute of CAS are acknowledged for

helpful discussions.

Conﬂicts of Interest: The authors declare no conﬂict of interest.

Remote Sens. 2021,13, 4784 18 of 19

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