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Scattering Mechanism Extraction by a Modified Cloude-Pottier Decomposition for Dual Polarization SAR

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Dual polarization is a typical operational mode of polarimetric synthetic aperture radar (SAR). However, few studies have considered the scattering mechanism extraction of dual-polarization SARs. A modified Cloude-Pottier decomposition is proposed to investigate the performance of the scattering mechanism extraction of dual-polarization SARs. It is theoretically demonstrated that only HH-VV SAR can discriminate the three canonical scattering mechanisms from an isotropic surface, horizontal dipole, and isotropic dihedral. Various experiments are conducted using 21 scenes from real datasets acquired by AIRSAR, Convair-580 SAR, EMISAR, E-SAR, Pi-SAR, and RADARSAT-2. Division of the dual-polarization H-α plane is experimentally obtained. The lack of cross-polarization induces the diffusion of scattering mechanisms and their overlap in the HH-VV H-α plane. However, the performance of HH-VV SAR for extracting scattering mechanisms is acceptable. Thus, HH-VV SAR is a suitable alternative to full-polarization SAR in certain cases. Meanwhile, the extraction performance of the other two dual-polarization SARs is badly degraded due to the lack of co-polarization. Therefore, HH-HV and HV-VV SARs cannot effectively extract the scattering mechanisms in the H-α plane.
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Remote Sens. 2015, 7, 7447-7470; doi:10.3390/rs70607447
remote sensing
ISSN 2072-4292
www.mdpi.com/journal/remotesensing
Article
Scattering Mechanism Extraction by a Modified Cloude-Pottier
Decomposition for Dual Polarization SAR
Kefeng Ji 1,†,* and Yonghui Wu 2,†
1 College of Electronics Science and Engineering, National University of Defense Technology,
Changsha 410073, China
2 Early Warning Academy, Wuhan 430019, China; E-Mail: wuxiaowu76@yahoo.com
These authors contributed equally to this work.
* Author to whom correspondence should be addressed; E-Mail: jikefeng@nudt.edu.cn;
Tel.: +86-731-8457-6350.
Academic Editors: Nicolas Baghdadi and Prasad S. Thenkabail
Received: 1 November 2014 / Accepted: 22 May 2015 / Published: 5 June 2015
Abstract: Dual polarization is a typical operational mode of polarimetric synthetic aperture
radar (SAR). However, few studies have considered the scattering mechanism extraction of
dual-polarization SARs. A modified Cloude-Pottier decomposition is proposed to investigate
the performance of the scattering mechanism extraction of dual-polarization SARs. It is
theoretically demonstrated that only HH-VV SAR can discriminate the three canonical
scattering mechanisms from an isotropic surface, horizontal dipole, and isotropic dihedral.
Various experiments are conducted using 21 scenes from real datasets acquired by AIRSAR,
Convair-580 SAR, EMISAR, E-SAR, Pi-SAR, and RADARSAT-2. Division of the
dual-polarization H-α plane is experimentally obtained. The lack of cross-polarization induces
the diffusion of scattering mechanisms and their overlap in the HH-VV H-α plane. However,
the performance of HH-VV SAR for extracting scattering mechanisms is acceptable. Thus,
HH-VV SAR is a suitable alternative to full-polarization SAR in certain cases. Meanwhile, the
extraction performance of the other two dual-polarization SARs is badly degraded due to the
lack of co-polarization. Therefore, HH-HV and HV-VV SARs cannot effectively extract the
scattering mechanisms in the H-α plane.
Keywords: polarimetry; dual polarization; synthetic aperture radar (SAR); scattering
mechanism; target decomposition
OPEN ACCESS
Remote Sens. 2015, 7 7448
1. Introduction
Polarimetric synthetic aperture radar (SAR) is an advanced instrument used in remote sensing tasks.
It has been widely applied in many fields, including ecology, environmental surveillance, and geological
exploration. Unlike single polarization, polarimetric SAR obtains scattering echoes from several
polarimetric channels and thus provides richer information than single polarization. This technique can
help improve edge extraction, segmentation, classification, target detection, and recognition. Scattering
mechanism extraction is enabled by obtaining datasets from several polarimetric channels. Thus, this
technique is helpful for explaining complex electromagnetic phenomenology. It is also a powerful tool
for SAR image interpretation.
Target decomposition is an important method for extracting scattering mechanisms. This approach
represents target scattering by several basic scattering mechanisms. Since 1970, this technique has
become an advanced research area in polarimetric SAR signal processing, with many valuable coherent
and incoherent decompositions being developed [1–16]. Among these methods, Cloude-Pottier
decomposition has attracted considerable attention. Cloude and Pottier calculated an entropy H and an
angle α and then linearly separated the H-α plane into nine zones within a feasible region to determine
the basic scattering mechanisms. In recent years, Cloude-Pottier decomposition has been analyzed,
improved, and widely applied in segmentation, classification, and detection applications [17–30].
These target decompositions are often used to analyze fully polarimetric SAR data. Few researchers
have considered the performance of compact SAR in scattering mechanism extraction [25,28]. Moreover,
there is minimal research on dual-polarization SARs [31,32].
Full and dual polarizations are two typical operational modes of polarimetric SAR. In fully
polarimetric mode, a scattering matrix containing the full scattering information of a target is measured
to reveal the scattering mechanisms of the target. Dual polarization is a frequently used operational mode
of polarimetric SAR systems. For spaceborne systems, such as the European ASAR, Japanese PALSAR,
German TerraSAR, and Italian COSMO-SkyMed, dual polarization is a reasonable mode for reducing
data volumes and simplifying technology.
Cloude-Pottier decomposition is often used to analyze fully polarimetric SAR data. Formulas and
parameters for dual-polarization SAR have been derived, but dividing lines in the H-α plane have not
been given [31]. In this paper, Cloude-Pottier decomposition is modified for dual-polarization SAR
applications. The discrimination performance for scattering mechanisms from an isotropic surface,
horizontal dipole, and isotropic dihedral is theoretically investigated for HH-VV, HH-HV, and HV-VV
SARs. The scattering mechanism extraction performance of dual-polarization SARs is analyzed using
21 scenes of real datasets acquired by six polarimetric SAR sensors, and optimal dividing lines of the
HH-VV, HH-HV, and HV-VV H-α planes are obtained. It is demonstrated that HH-VV SAR can
effectively extract eight scattering mechanisms in the dual-polarization H-α plane despite the lack of
cross-polarization, whereas HH-HV and HV-VV SARs can only partially extract low, medium, and high
entropy scattering mechanisms due to the lack of co-polarization.
The remainder of this paper is structured as follows. Cloude-Pottier decomposition is briefly
introduced in Section 2 and modified for dual-polarization cases in Section 3. In Section 4, the
performance of dual-polarization SARs in extracting several canonical scattering mechanisms is
Remote Sens. 2015, 7 7449
theoretically discussed using the modified decomposition, which is followed by the experimental results
and discussion in Section 5 and conclusions in Section 6.
2. Cloude-Pottier Decomposition
Assuming that the reciprocity principle is satisfied, a complex scattering matrix measured by fully
polarimetric SAR is expressed as
(1)
Using the Pauli bases to decompose the scattering matrix, the scattering vector
k=SHH+SVV SHHSVV 2SHVT2
can be derived, where the superscript “T” denotes the matrix
transpose. The coherency matrix is defined as
(2)
where L is the number of looks, ki is the -th look sample of k, the superscript “H” denotes the complex
conjugate transpose, and denotes the assembly average. T can be decomposed into
(3)
where q is the number of polarimetric channels, given here as q=3; λi are eigenvalues of T, with
λ1≥λ2≥λ3; and ui=ejφicosαisinαicosβiejδisinαisinβiejγiT
are eigenvectors. αi denote the
scattering mechanisms of a target, βi are the orientation angles, and φi, δi, and γi are the phases.
An entropy H and angle α describing the averaged scattering mechanisms are defined as [16]
(4)
(5)
(6)
The target scattering behavior can be determined based on the target location on the plane constructed
using H and α. The division of the H-α plane and corresponding physical properties of each zone are
shown in Figure 1.
The region between the two curves represents the feasible region in Figure 1. The value (H,α)
calculated for any target is located inside this feasible region. Curves 1 and 2 are determined by
(7)
HH HV
HV VV
SS
SS
S
H
1
1L
ii
i
L
Tkk
i
H
1
q
iii
i

Tuu

1
log
q
iqi
i
H
PP

1
q
ii
i
P

1
i
iq
j
j
P
1
10 0
00, 01
00
mm
m






T
Remote Sens. 2015, 7 7450
(8)
where m is a boundary parameter.
Figure 1. Division of the full-polarization H-α plane and physical properties.
3. Modification of Cloude-Pottier Decomposition for Dual-Polarization SAR Applications
Cloude-Pottier decomposition is proposed for fully polarimetric SAR. In this paper, this technique is
modified to analyze the scattering mechanism extraction performance of dual-polarization SARs. The
modified visions for three dual-polarization SARs, HH-VV, HH-HV, and HV-VV, are discussed, and a
new boundary of the feasible region in the H-α plane for these cases is derived in this section.
The HH-VV SAR scattering matrix is
(9)
and the corresponding scattering vector based on the Pauli matrices is
(10)
where PS and Pk are the total powers of S and k, respectively.
The coherency matrix is
(11)
THH-VV can be decomposed into
(12)
2
2
00 0
0 1 0 , 0 0.5
002
2100
0 1 0 , 0.5 1
001
m
m
m
m





 






T
T
HH
VV
0
0
S
S
S

TT
HH VV HH VV HH VV HH VV
11
00
22
SSSS SSSS   kk
H
HH VV
1
1L
ii
i
L
Tkk
2
H
HH VV
1
iii
i

Tuu
Remote Sens. 2015, 7 7451
where λi(i=1,2) are the eigenvalues of THH-VV, with λ1≥λ2. ui=ejφicosαisinαicosβiejδiT
are
eigenvectors, αi denote the scattering mechanisms of the target, βi are the orientation angles, and φi and
δi are the phases.
The parameters H and α are
(13)
(14)
(15)
Using a similar method as that for full polarization, the dual-polarization H-α plane can be divided
into several zones to discriminate different scattering mechanisms. The details are discussed in
Section 5.
The HH-HV SAR scattering matrix is
(16)
and the corresponding scattering vector is
(17)
The scattering matrix and corresponding scattering vector of HV-VV SAR are, respectively,
(18)
and
(19)
(H,α) for HH-HV and HV-VV SAR data can be calculated using the derivation presented above for
HH-VV SAR.
Considering the extreme value of (H,α) for dual-polarization SAR applications, the boundary of the
feasible region in the H-α plane is modified by [31].
(20)
(21)
The new boundary is symmetrical with respect to α=45°, as shown in Figure 2.
4. Extraction of Several Canonical Scattering Mechanisms
Cloude and Pottier used α for the scattering mechanisms [16]. α=0°,45°,90° denotes scattering from
an isotropic surface, horizontal dipole, and isotropic dihedral, respectively. The abilities of HH-VV,

2
2
1
log
ii
i
HPP

2
1
ii
i
P

2
1
i
i
j
j
P
HH HV
HV 0
SS
S
S
T
HH HV
2SSk
HV
HV VV
0S
SS
S
T
VV HV
2SSk
1
10
, 0 1
0m
m




T
2
0, 0 1
01
mm




T
Remote Sens. 2015, 7 7452
HH-HV, and HV-VV SARs to discriminate these three scattering mechanisms are analyzed in this
section. For simplicity, only the horizontal dipole and dihedral are considered.
In the case of full polarization, the scattering matrices for an isotropic surface, horizontal dipole, and
isotropic dihedral are
(22)
According to Equations (10) and (11), the three corresponding scattering vectors and coherency
matrices for HH-VV SAR are
(23)
(24)
One can find that
(25)
The scattering vectors of the three elementary targets for HH-HV SAR are derived from
Equations (17) and (22) as
(26)
According to Equations (19) and (22), the scattering vectors of the targets for HV-VV SAR are
(27)
The three elementary targets present canonical scattering mechanisms in the full- and dual-polarization
H-α planes, as shown in Figure 2.
Figure 2. Three canonical scattering mechanisms presented by elementary targets in the
full- and dual-polarization H-α planes. (a) Full polarization; (b) HH-VV; (c) HH-HV;
(d) HV-VV.
The positions of the three canonical scattering mechanisms in Figure 2b are identical to those in
Figure 2a. The three mechanisms can be discriminated by HH-VV SAR using α, even though the values
of H are zero. Nevertheless, they cannot be separated in Figure 2c,d. (H,α) of the three targets for
HH-HV SAR is (0,0°). In addition, (H,α) of the dipole for HV-VV SAR cannot be calculated. For the other
sf dp dh
10 10 1 0
,,
01 00 0 1
   

   
   
SSS
TTT
sf dp dh
20, 2222, 02
 
 
 
kk k
sf dp dh
20 11 00
1
,,
00 11 02
2
  
 
  
  
TT T
dp
sf dh
dp
sf dh
0
00
, ,
45
090
H
HH


 
 
  

T
10k
TT T
sf dp dh
10, 00, 10 kk k
Remote Sens. 2015, 7 7453
two targets, (H,α)=(0,0°), HH-HV and HV-VV SARs cannot discriminate the three canonical
scattering mechanisms.
5. Experimental Results and Discussion of Scattering Mechanism Extraction for
Dual-Polarization SARs
The coherency matrix T of fully polarimetric SAR can be expressed as
(28)
The eigenvalues are [33]
(29)
where , , and are
(30)
Here, Tr(·) and |·| denote the trace and determinant of a matrix, respectively.
The coherency matrix THH-VV of HH-VV SAR is
(31)
The corresponding eigenvalues can be derived as
(32)
where Tr(THH-VV) and Tr2(THH-VV) are

 
 
2
HH VV HH VV HH VV HH VV VV
2
HH VV HH VV HH VV HH VV VV
2
VV HH VV VV HH VV VV
12
13
23
1
2
SS SSSS SSS
SS SS SS SSS
SS S SS S S
azz
zbz
zz c






 









T





11
33
111
33
1
3
221 1
33 3
1
3
321 1
33 3
11 2
Tr
23 332
1j3 1j3
11
Tr
23 32 62
1j3 1j3
11
Tr
23 32 62
BC
C
B
C
C
B
C
C


  






  







  




T
T
T
AB C
 

 

11 2 2 33
22 2
11 2 2 33
2
33
3
333
27 9 Tr 2 Tr 27 9 Tr 2 Tr 4
Aabacbczzzzzz
Ba abb acbcc zz zz zz
CA A B


 
 
    TTT TTT


2
HH VV HH VV HH VV
HH VV 2
HH VV HH VV HH VV
1
2
SS SSSS
SSSS SS




 

T



2
HH VV HH VV 2 HH VV
1Tr Tr 4Tr
2 

 


TT T
Remote Sens. 2015, 7 7454
(33)
Equations (4), (6), and (28)–(30) indicate that H is a function of elements of the coherency matrix
T for fully polarimetric SAR. Thus, can be expressed as Hf (SHH,SHV,SVV). Equations (13), (15),
and (31)–(33) show that this is the same for HH-VV SAR, and HHH-VV(SHH,SVV) is obtained. Similarly,
HHH-HV(SHH,SHV) and HHV-VV(SHV,SVV) are derived for HH-HV and HV-VV SARs.
Considering the dividing line Hf (SHH,SHV,SVV)=0.5 between low and medium entropy scattering in
the full-polarization H-α plane, the corresponding dividing line HHH-VV(SHH,SVV)=K is set in the HH-VV
H-α plane. Because of the lack of restrictions, K cannot be derived from Hf (SHH,SHV,SVV)=0.5, and
analytic representations of all dividing lines in the HH-VV H-α plane cannot be derived. The cases for
HH-HV and HV-VV are similar.
Various experiments are conducted to validate the conclusion above. The distribution of scatters
around each dividing line of the full-polarization H-α plane in three dual-polarization planes is shown in
Figure 3. Figure 3a–d correspond to the narrow group, where the width of two dividing lines for H is
0.0014, and the width of five dividing lines for α is 0.2. Figure 3e–h correspond to the wide group, where
the widths for H and α are 0.02 and 4, respectively. Figure 3a,e are scattering plots of the dividing lines
in the full-polarization H-α plane. The corresponding plots in the HH-VV, HH-HV, and HV-VV H-α
planes are shown in Figure 3b–d and (f)–(h). A NASA/JPL AIRSAR L-band image of San Francisco,
4-look processed, is used herein. The size of the filtering windows is 5 × 5.
Figure 3. Dual-polarization distribution of full-polarization dividing lines. (a) Scattering
plots of dividing lines in the full-polarization H-α plane for the narrow group; (b) HH-VV
distribution of scatters in (a); (c) HH-HV distribution of scatters in (a); (d) HV-VV
distribution of scatters in (a); (e) Scattering plots of dividing lines in the full-polarization
H-α plane for the wide group; (f) HH-VV distribution of scatters in (e); (g) HH-HV
distribution of scatters in (e); (h) HV-VV distribution of scatters in (e).



22
HH VV HH VV HH VV
22
2HHVV HHVV HH VV
HH VV HH VV HH VV HH VV
1
Tr 2
1
Tr 2
SS SS
SS SS
SSSS SSSS


 
   
T
T
H
Remote Sens. 2015, 7 7455
Figure 3 shows that the dividing lines irregularly diffuse in three dual-polarization H-α planes. The
diffusing range is similar for both groups. The diffusing range in the dual-polarization H-α planes of the
top group does not focus, and the width of the dividing lines is narrower than that of the lower group.
Although the scattering plots in Figure 3a,e are not real dividing lines but simply various scatters around
the real lines, the irregular diffusion illustrates that the dividing lines inevitably become dispersive
scatters when they project from the full-polarization H-α plane to the dual-polarization planes.
Substantially more data acquired by AIRSAR, Convair-580 SAR, EMISAR, E-SAR, Pi-SAR, and
RADARSAT-2 are applied in further experiments. The results are highly similar.
Therefore, the dividing lines in the dual-polarization H-α planes are determined and experimentally
validated in this section. A total of 21 data scenes are used. Certain scenes are multi-look processed to
obtain 31 datasets. Then, all data are filtered by rectangular windows of 5 sizes: 3 × 3, 5 × 5, 7 × 7,
9 × 9, and 11 × 11. Thus, 31 × 5 datasets are produced. Information about the data is listed in Table 1.
The data for Nos. 11 and 18 are used for testing, and the others are used for training. The training data
are applied to obtain the optimal dividing lines in the three dual-polarization H-α planes.
Table 1. Description of the training and testing data.
Number Sensor Scene Size Number of Looks Usage
1 AIRSAR San Francisco 900 × 1024 4 training
2 AIRSAR Flevoland 750 × 1024 4 training
3 AIRSAR Death Valley 1279 × 1024 4 training
4 Convair-580 SAR Ottawa 222 × 342 100 training
5 EMISAR Foulum 1750 × 1000 1 training
6 EMISAR Foulum 875 × 1000 2 training
7 EMISAR Foulum 875 × 500 4 training
8 EMISAR Foulum 437 × 500 8 training
9 E-SAR Oberpfaffenhofen top 1408 × 1540 1 training
10 E-SAR Oberpfaffenhofen top 704 × 770 4 training
11 E-SAR Oberpfaffenhofen down 1408 × 1540 1 testing
12 Pi-SAR Niigata 1200 × 1200 1 training
13 Pi-SAR Niigata 600 × 600 4 training
14 Pi-SAR Tsukuba top 1000 × 2000 1 training
15 Pi-SAR Tsukuba top 500 × 1000 4 training
16 Pi-SAR Tsukuba down 1000 × 2000 1 training
17 Pi-SAR Tsukuba down 500 × 1000 4 training
18 RADARSAT-2 San Francisco 550 × 750 8 testing
19 RADARSAT-2 Altona1 800 × 800 1 training
20 RADARSAT-2 Altona2 900 × 900 1 training
21 RADARSAT-2 Flevoland1 800 × 800 1 training
22 RADARSAT-2 Flevoland1 400 × 400 4 training
23 RADARSAT-2 Flevoland2 900 × 900 1 training
24 RADARSAT-2 Oberpfaffenhofen1 800 × 800 1 training
25 RADARSAT-2 Oberpfaffenhofen1 400 × 400 4 training
26 RADARSAT-2 Oberpfaffenhofen2 1000 × 1000 1 training
27 RADARSAT-2 Gibraltar 900 × 900 1 training
28 RADARSAT-2 Vancouver1 1001 × 1110 1 training
29 RADARSAT-2 Vancouver2 800 × 800 1 training
30 RADARSAT-2 Vancouver3 800 × 800 1 training
31 RADARSAT-2 Vancouver3 400 × 400 4 training
Remote Sens. 2015, 7 7456
5.1. Optimal Dividing Lines in the Dual-Polarization H-α Planes
The above 4-look NASA/JPL AIRSAR L-band image of San Francisco is shown in Figure 4a. There
are four terrain types: sea, mountains, forests, and buildings. Figure 4b is the scattering plot in the
full-polarization H-α plane, and the corresponding plots in three dual-polarization H-α planes are shown
in Figure 4c–e. In the last three plots, the color of each scatter is determined by that in Figure 4b. For
example, red scatters in Z6 in Figure 4b are also colored red wherever they diffuse in Figure 4c–e. Scatters
with different colors in Figure 4c–e are plotted in sequence from Z1 to Z9.
The scatters in each zone of the full-polarization H-α plane clearly diffuse in the three dual-polarization
planes. In Figure 4c, scatters with different colors can also be partitioned. Nevertheless, they exhibit
strong further overlap with each other.
In Figure 4c, although the eight scattering mechanisms determined by the full-polarization H-α plane
diffuse and overlap to a certain extent in the HH-VV H-α plane, they can still be classified overall.
All three low entropy scattering mechanisms diffuse rightward. Low entropy multiple scattering
diffuses downward and overlaps with the low entropy surface and dipole scattering.
Three medium entropy scattering mechanisms diffuse rightward. Medium entropy dipole and multiple
scattering mechanisms diffuse downward; thus, medium entropy dipole scattering overlaps with the
other two medium entropy scattering mechanisms. The majority of the medium entropy scatters can be
separated from low entropy scatters.
Figure 4. Scattering plot in the full- and dual-polarization H-α planes. (a) Color-coded Pauli
reconstructed and Google Earth images; (b) Full polarization; (c) HH-VV; (d) HH-HV; (e)
HV-VV.
Remote Sens. 2015, 7 7457
High entropy scatters do not overlap with low entropy scatters. High entropy dipole scattering partly
overlaps with medium entropy surface and multiple scattering and strongly with medium entropy dipole
scattering. High entropy multiple scattering can be well separated from medium entropy surface
scattering. However, it partially overlaps with medium entropy dipole scattering and strongly with
medium entropy multiple scattering. Namely, two high entropy scattering mechanisms are confused with
two corresponding medium entropy scattering mechanisms. Furthermore, high entropy scatters partially
overlap with each other.
For HH-HV SAR applications, scattering mechanisms cannot be effectively divided by in
Figure 4d. Medium and low entropy scattering mechanisms are highly confused. High entropy scattering
mechanisms are completely covered by medium entropy dipole and multiple scattering. As observed in
Figure 4e, the case for HV-VV SAR is similar to that for HH-HV.
Similar to the case of full polarization, there are also seven dividing lines within the feasible region
of the dual-polarization H-α plane. These lines are numbered as follows:
(1) Line 1, l1, for dividing low and medium entropy zones;
(2) Line 2, l2, for dividing medium and high entropy zones;
(3) Line 3, l3, for dividing Z1 and Z2;
(4) Line 4, l4, for dividing Z2 and Z3;
(5) Line 5, l5, for dividing Z4 and Z5;
(6) Line 6, l6, for dividing Z5 and Z6;
(7) Line 7, l7, for dividing Z8 and Z9.
Figure 4 shows that all scattering mechanisms diffuse and overlap in the dual-polarization H-α plane.
The optimal dividing line should induce the least number of scatters in false zones, namely,
(34)
where li is the i-th dividing line, n(li) is the total number of scatters in false zones induced by li, and nj(li)
is the number of scatters of the j-th scattering mechanism in false zones induced by li. The value of j
varies for different dividing lines. Specifically, j=6 is for l1, with Z1-6 involved; j=5 is for l2, with Z4-6,
Z8, and Z9 involved; j=2 is for l37, and only two zones above and below the dividing line would be
considered. For example, j=2 is for l3, with only Z1 and Z2 involved.
The number of scatters for each scattering mechanism in the H-α plane is different. Although the
difference is large, the optimal line derived using Equation (34) should classify nearly all scattering
mechanisms with fewer scatters into that with more scatters. To avoid this case, nj(li) is weighted. The
weight is inversely proportional to the number of scatters of each scattering mechanism. Thus, Equation (34)
is modified as follows:
(35)
where wj=Nmax/Nj is the weight, Nmax is the greatest number of scatters among the eight scattering
mechanisms, and Nj is the number of scatters of the j-th scattering mechanism.
Although scattering mechanisms cannot be effectively divided by HH-HV and HV-VV SARs, as
shown in Figure 4d,e, they are also analyzed along with HH-VV for further comparison. The number of

opt arg min arg min , 1, 2, 7
ii
ii ji
ll
j
lnl nli 
  
max
opt arg min arg min arg min , 1, 2, 7
ii i
ii ji jji
ll l
jj
j
N
lnl nl wnli
N
 

Remote Sens. 2015, 7 7458
scatters in false zones is plotted as a function of li(i=1,2,…,7) for HH-VV SAR in Figure 5.
Figure 5a–c are lines 1 and 2 of HH-VV, HH-HV, and HV-VV, whereas Figure 5d–f are lines 3–7.
Figure 5. Curves of the number of scatters in false zones as a function of li (i = 1,2,.…,7) of
dual-polarization SARs using AIRSAR San Francisco data. (a) Lines 1 and 2 of
HH-VV; (b) Lines 1 and 2 of HH-HV; (c) Lines 1 and 2 of HV-VV; (d) Lines 3-7 HH-VV;
(e) Lines 3-7 HH-HV; (f) Lines 3-7 HV-VV.
The curves in Figure 5a–c are V-shaped. This indicates that three dual-polarization SARs can partially
partition low, medium, and high entropy scattering mechanisms. The curves in Figure 5d are regular
V-shaped, whereas the curves are comparatively irregular in Figure 5e,f. The minimum of each curve in
Figure 5d is considerably lower than that in Figure 5e,f. The minimum values of lines 3 and 5 are on the
left, and the corresponding values of lines 4 and 6 are on the right of Figure 5d. This situation is consistent
with the position of the dividing line in the full-polarization H-α plane, whereas it is reversed in
Figure 5e. Lines 3 and 4 are irregular with several points of intersection, and line 6 is higher than line 5
in Figure 5f. This predicates that HH-VV SAR can partition surface, dipole, and multiple scattering
mechanisms better than can HH-HV and HV-VV SARs. Many other datasets are applied in further
experiments, and highly similar curves are observed.
The optimal dividing lines for three dual-polarization H-α planes obtained using 29 × 5 training
datasets are shown as dashed lines in Figure 6. Bolded solid lines denote the average values listed in
Table 2.
The HH-VV optimal dividing lines congregate in Figure 6a. The separating degree of two clusters of
dividing lines for H in Figure 6a is higher than that in the other two figures. The dividing lines for α do
not overlap and are located in the feasible region in the HH-VV H-α plane. However, the lines strongly
diffuse and overlap in the other two planes, and some are outside of the feasible region. Moreover, two
average lines in the low entropy zone are inverted in the HH-HV plane. In Table 2, the difference in H
between three dual-polarization SARs is less than that in α. Figure 6 and Table 2 show that HH-VV SAR
extracts the eight scattering mechanisms more effectively than do HH-HV and HV-VV SARs. The latter
Remote Sens. 2015, 7 7459
two SARs can only partition low, medium, and high entropy scatters to a certain extent and poorly
discriminate surface, dipole, and multiple scatters.
Figure 6. Optimal dividing lines in the dual-polarization H-α plane. (a) HH-VV;
(b) HH-HV; (c) HV-VV.
Table 2. Average of the optimal dividing lines in the dual-polarization H-α plane.
l1opt l2opt l3opt
(°)
l4opt
(°)
l5opt
(°)
l6opt
(°)
l7opt
(°)
HH-VV 0.64 0.90 34.0 46.7 31.8 44.2 43.9
HH-HV 0.66 0.93 33.5 31.3 38.1 48.4 50.2
HV-VV 0.69 0.94 26.1 49.1 37.8 53.0 53.8
5.2. Scattering Mechanism Retention Ratio of Dual-Polarization SARs
The previous experimental results illustrate that all scattering mechanisms diffuse in the dual-polarization
H-α plane. Thus, certain scatters are inevitably labeled as a false scattering mechanism. For the
quantitative analysis, the scattering mechanism retention ratio is defined herein as
(36)
where Nfd is the number of scatters with the scattering mechanism in the dual-polarization H-α plane
being the same as that in the full-polarization H-α plane, and Nf is the number of scatters with the
corresponding scattering mechanism in the full-polarization H-α plane.
The overall scattering mechanism retention ratio is the average of all scattering mechanism
retention ratios
(37)
where Rr,j is the scattering mechanism retention ratio of the j-th scattering mechanism.
The scattering mechanism retention ratios of three dual-polarization SARs are calculated using the
datasets listed in Table 1 and the average optimal dividing lines in Figure 6 and Table 2. The results are
shown in Figure 7. Ramean in the legend denotes the average retention ratio of 31 × 5 datasets, and
3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11 are the sizes of the filtering windows. Ramean and the average
retention ratios corresponding to the five filtering windows are listed in Table 3.
f
d
r
f
N
RN
8
,
1
1
8
arj
j
R
R
Remote Sens. 2015, 7 7460
Figure 7. Scattering mechanism retention ratios of three dual-polarization SARs
corresponding to average optimal dividing lines. (a) HH-VV; (b) HH-HV; (c) HV-VV.
Table 3. Average scattering mechanism retention ratios of three dual-polarization synthetic
aperture radars (SARs).
Average Scattering Mechanism Retention Ratio HH-VV HH-HV HV-VV
Ramean 67.74 29.32 29.87
3 × 3 66.10 28.59 28.72
5 × 5 68.00 29.45 30.07
7 × 7 68.36 29.54 30.21
9 × 9 68.23 29.67 30.08
11 × 11 67.99 29.34 30.26
The average scattering mechanism retention ratio of HH-VV SAR is 67.74%. Nevertheless, the
corresponding values for HH-HV and HV-VV SARs are less than 30%. This observation indicates that
only HH-VV SAR can preserve the scattering mechanism. In Figure 7, five curves interlace for three
dual-polarization SARs. The maximum average values correspond to 7 × 7, 9 × 9, and 11 × 11 in
Table 3, and the minimum average values correspond to 3 × 3. The difference between the maximum
and minimum average values is not large, indicating that the size of the windows does not significantly
affect the scattering mechanism retention ratios. Figure 7 and Table 3 show that multi-look processing
does not significantly affect the optimal dividing lines.
The confusion matrixes of the average scattering mechanism retention ratios corresponding to
Figure 7a–c are listed in Tables 4–6.
Table 4. Confusion matrix of average scattering mechanism retention ratios Rr (%) of HH-VV.
Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9
Z1 90.94 7.97 0 0.40 0.68 0 0 0
Z2 5.88 84.58 0.84 0.32 5.15 3.23 0 0
Z3 0.97 5.74 84.64 0.08 0.33 8.20 0.01 0.03
Z4 30.92 1.01 0 52.53 12.29 0 3.26 0
Z5 1.26 3.08 0.11 14.71 39.23 4.76 30.74 6.12
Z6 0.09 0.92 4.40 0.48 7.35 48.79 4.05 33.92
Z8 0.02 0.02 0.01 9.12 12.75 0.85 65.62 11.62
Z9 0 0.02 0.30 0.05 2.74 9.56 11.75 75.58
Remote Sens. 2015, 7 7461
Table 5. Confusion matrix of average scattering mechanism retention ratios Rr (%) of HH-HV.
Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9
Z1 62.10 0 2.59 33.26 0.98 0.16 0.90 0.00
Z2 73.32 0 14.42 7.22 1.16 2.79 0.98 0.10
Z3 78.44 0 17.61 2.69 0.60 0.50 0.15 0.01
Z4 11.08 0 0.96 53.12 6.45 0.68 27.53 0.18
Z5 10.80 0 2.09 36.55 10.82 4.89 33.61 1.23
Z6 20.29 0 7.40 37.56 11.77 8.50 13.93 0.55
Z8 0.00 0 0.02 0.01 3.01 15.47 70.10 11.39
Z9 0.06 0 0.75 0 3.33 43.84 39.73 12.29
Table 6. Confusion matrix of average scattering mechanism retention ratios Rr (%) of HV-VV.
Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9
Z1 74.74 5.71 0.61 16.78 1.57 0.14 0.44 0.00
Z2 27.30 13.47 8.10 21.33 9.46 6.04 14.03 0.27
Z3 40.90 20.69 9.58 15.14 7.59 2.70 3.32 0.07
Z4 15.19 2.81 0.15 47.86 9.34 0.34 24.29 0.02
Z5 7.46 2.57 1.29 24.88 18.31 6.76 38.15 0.58
Z6 12.45 6.28 5.72 27.20 20.51 10.78 16.67 0.39
Z8 0.01 0.01 0.08 0.00 12.14 22.68 62.22 2.86
Z9 0 0.06 3.30 0 15.11 46.81 32.73 1.99
In Tables 4–6, diagonal bold numbers are the percentage of scatters with correct scattering mechanism
in dual-polarization H-α planes; bold italic numbers are the greatest values, except for the diagonal in a
line, thus revealing the dominant diffusing direction; and underlined bold italic numbers are the values
greater than the diagonal in a line, thus revealing the dominant transfer direction and indicating that
scatters transferring out are more prominent than those remaining in the correct zone. The dominant
diffusing and transfer directions, represented by bold italic and underlined bold italic numbers, respectively,
are shown in Figure 8. The meaning of the serial number of each zone is the same as that in Figure 1.
The dividing lines are determined using Table 2. Black arrows indicate the dominant diffusing directions,
and green arrows indicate the dominant transfer directions.
Figure 8. Dominating diffusing and transfer directions of scattering mechanisms. (a)
HH-VV; (b) HH-HV; (c) HV-VV.
Remote Sens. 2015, 7 7462
The diagonal elements are the greatest values in each line, with six values higher than 50%, and there
are only three lines where the second highest values exceed 30% in Table 4. This predicates that most
scatters in the full-polarization H-α plane are located in corresponding zones in the HH-VV H-α plane.
Therefore, HH-VV SAR can effectively extract scattering mechanisms. Although scatters in the center
zone Z5 diffuse to the greatest extent, Rr is nearly 40%. Figure 8a illustrates that only Z1 and Z8 have
two dominant diffused directions, whereas the others only have one. This indicates that scatters do not
strongly overlap in the HH-VV H-α plane.
Among the eight diagonal elements in Table 5, only the values in Z1, Z4, and Z8 are the highest in
their line, and they are higher than 50%. This indicates that only scatters of these three zones in the
full-polarization H-α plane are located mainly in corresponding zones in the HH-HV H-α plane.
Diagonal elements in other zones are lower than 20%, with the smallest value below 10%. The values
are all considerably smaller than the greatest value in their lines, indicating that scatters of these zones
in the full-polarization H-α plane transfer nearly completely out of the corresponding zones in the
HH-HV H-α plane. Table 5 and Figure 8b illustrate that transfer induces scatters in Z3, Z5 and Z6, and
Z9 overlapping with those in Z1, Z4, and Z6, respectively. Therefore, HH-HV cannot effectively extract
scattering mechanisms. In addition, elements in the second column are all zero because l3opt>l4opt for
HH-HV in Table 2; therefore, Z2 does not exist in this case.
The case of Figure 8c and Table 6 is highly similar to that of Figure 8b and Table 5, except that
elements in the second column of Table 6 are not zero and the dominating transfer direction of Z5 is to
Z8. Figure 8c and Table 6 also indicate that HV-VV SAR cannot discriminate scattering mechanisms
due to considerable scatter transferring and overlapping.
5.3. Comparison of Extraction Performance between Full- and Dual-Polarization SARs
(1) AIRSAR San Francisco data
The classification map of fully polarimetric San Francisco data using Cloude-Pottier decomposition
is shown in Figure 9a, with the color code in Figure 4b. Figure 4b is plotted again in Figure 9e for clarity.
The classification maps of the corresponding HH-VV, HH-HV, and HV-VV data using the modified
Cloude-Pottier decomposition are shown in Figure 13b–d, with the color code in Figure 13f–h. The size
of the filtering windows is N=5 herein. The corresponding scattering mechanism retention ratios are
listed in Table 7.
Table 7. Scattering mechanism retention ratios Rr (%) of AIRSAR San Francisco data.
Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9 Average
HH-VV 99.46 86.92 90.20 55.82 21.90 45.03 64.05 83.59 68.37
HH-HV 77.75 0 57.38 35.42 19.89 5.67 38.52 10.82 30.68
HV-VV 99.52 25.38 19.71 39.64 17.45 2.95 70.57 3.10 34.79
Terrains with different scattering mechanisms, such as sea terrain with low entropy surface scattering,
mountain terrain with medium entropy surface scattering, buildings with medium entropy multiple
scattering, and forests with high entropy dipole scattering, can be effectively discriminated by
Cloude-Pottier decomposition for fully polarimetric applications, as shown in Figure 9a.
Remote Sens. 2015, 7 7463
Figure 9. Classification maps of AIRSAR San Francisco data (N = 5). (a) Full polarization;
(b) HH-VV; (c) HH-HV; (d) HV-VV; (e) Color code for full polarization; (f) Color code for
HH-VV; (g) Color code for HH-HV; (h) Color code for HV-VV.
Figure 9 and Table 7 show that the performance of HH-VV SAR for extracting scattering mechanisms
exceeds those of HH-HV and HV-VV SARs. Four terrains can also be classified by the modified
Cloude-Pottier decomposition for HH-VV SAR data. Moreover, the extraction performance for sea,
mountains, forests, and mid-right 45° buildings is comparable with that of fully polarimetric SAR. The
average retention ratio of HH-VV is 68.37%, and the corresponding values for HH-HV and HV-VV are
nearly half of that value. Only the retention ratios of Z5 and Z6 are less than 50% for HH-VV. This
indicates the following: (1) the medium entropy dipole scatters (blue) of the building area and lower left
coast in Figure 9a become other mechanisms in Figure 9b; and (2) the medium entropy multiple scatters
(red) of the city in Figure 9a become high entropy multiple scatters (orange) in Figure 9b.
Compared with Figure 9b, Figure 9c,d illustrate that the performance of the extracting scattering
mechanism for HH-HV and HV-VV SARs is worse. Although four terrains can be differentiated, the
scattering mechanisms are greatly confused. Only the retention ratios of Z1 and Z3 are higher than 50%
for HH-HV in Table 7. Correspondingly, the low entropy surface scatters of the upper sea area in
Figure 9c are acceptable. However, the low entropy multiple scatters of the building area in Figure 9c
are higher than those in Figure 9a due to other scatters transferring into Z3. Only the retention ratios of
Z1 and Z8 are higher than 50% for HV-VV. Consequently, the low entropy surface scatters of the sea
area and high entropy dipole scatters of the forest area in Figure 9d are acceptable. Furthermore,
HH-HV and HV-VV SARs poorly extract other scattering mechanisms.
Remote Sens. 2015, 7 7464
Mile Rock, Alcatraz Island, and the Golden Gate Bridge are indicated by A, B, and C in Figure 9a,
respectively. More detailed images of these areas are provided below. A flat-roofed, cylindrical lighthouse
is the only building at Mile Rock. The roof is set up as a helipad. There are several low buildings, a water
tower, and a lighthouse on Alcatraz Island. The Golden Gate Bridge is composed of a deck, two piers,
and many cables. The basic scattering mechanisms of the three objects are well extracted by HH-VV
SAR. In particular, low and medium entropy multiple scattering mechanisms, denoting polyhedral
characteristics of buildings, are identified by HH-VV SAR and fully polarimetric SAR, whereas
HH-HV and HV-VV SARs cannot extract the crucial scattering mechanisms of the three targets.
(2) E-SAR Oberpfaffenhofen data
The No. 11 and No. 18 training datasets in Table 1 are L-band 1-look data of Oberpfaffenhofen and
C-band 8-look data of San Francisco acquired by DLR E-SAR and CSA-MDA RADARSAT-2,
respectively, as shown in Figure 10.
Figure 10. Color-coded Pauli reconstructed and Google Earth images of No. 11 and No. 18
training data. (a) No. 11, E-SAR Oberpfaffenhofen data; (b) No. 18, RADARSAT-2 San
Francisco data.
Remote Sens. 2015, 7 7465
An airport, farmland, and various buildings are shown in Figure 10a. The terrains in Figure 10b are
the same as those in Figure 4a: sea, mountains, forests, and buildings.
The classification maps of the full- and dual-polarization Oberpfaffenhofen data using Cloude-Pottier
decomposition and the modified version are shown in Figure 11a–d, with the color code in Figure 11e–h.
The size of the filtering windows is N=9. The corresponding scattering mechanism retention ratios are
listed in Table 8.
Table 8. Scattering mechanism retention ratios Rr (%) of E-SAR Oberpfaffenhofen data.
Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9 Average
HH-VV 80.64 95.59 85.14 46.97 56.67 48.33 61.90 74.21 68.68
HH-HV 61.17 0 16.65 76.27 15.20 13.29 55.36 12.53 31.31
HV-VV 61.03 8.68 11.10 56.92 21.20 16.69 45.66 1.53 27.85
The performance of HH-VV SAR for extracting scattering mechanisms is closest to that of fully
polarimetric SAR, with an average retention ratio of 68.68% in Table 8; the majority of scatters are
correctly discriminated in Figure 11b. However, the majority of scatters are assigned incorrect labels
by HH-HV and HV-VV SARs in Figure 11c,d, and the retention ratios are less than half of that of
HH-VV SAR.
Figure 11. Classification maps of E-SAR Oberpfaffenhofen data (N = 9). (a) Full
polarization; (b) HH-VV; (c) HH-HV; (d) HV-VV; (e) Color code for full polarization; (f)
Color code for HH-VV; (g) Color code for HH-HV; (h) Color code for HV-VV.
Several objects are denoted by D, E, F, and G in Figure 11a. These objects are magnified in the images
below. Area D, labeled as medium entropy surface scattering, is clearly presented in Figure 11a. It is
confused with area E in Figure 11b because the medium entropy surface scattering diffuses to the
Remote Sens. 2015, 7 7466
medium entropy dipole scattering mechanism in area D. The scattering mechanisms of areas D and E
are differently labeled such that the two areas can be discriminated.
The five visible targets with dominate low entropy multiple scattering in area F in Figure 11a are
correctly and clearly displayed by HH-VV SAR in Figure 11b. These targets are set apart with false
scattering mechanisms, low entropy surface scattering, in Figure 11c. They cannot be differentiated from
the background in Figure 11d.
The target with low entropy surface scattering in area G is labeled with the correct mechanism in
Figure 11b. The contour of the target is clear, whereas the scattering mechanism is incorrect in Figure 11c,d.
(3) RADARSAT-2 San Francisco data
The classification maps of the full- and dual-polarization RADARSAT-2 San Francisco data using
Cloude-Pottier decomposition and the modified version are shown in Figure 12a–d, with the color code
in Figure 12e–h. The size of the filtering windows is N=5. The scattering mechanism retention ratios are
listed in Table 9.
Figure 12. Classification maps of RADARSAT-2 San Francisco data (N = 5). (a) Full
polarization; (b) HH-VV; (c) HH-HV; (d) HV-VV; (e) Color code for full polarization; (f)
Color code for HH-VV; (g) Color code for HH-HV; (h) Color code for HV-VV.
Table 9. Scattering mechanism retention ratios Rr (%) of RADARSAT-2 San Francisco data.
Z1 Z2 Z3 Z4 Z5 Z6 Z8 Z9 Average
HH-VV 99.61 74.61 73.90 68.89 22.99 59.20 72.01 67.74 67.37
HH-HV 98.69 0 5.36 30.38 2.23 4.41 69.32 7.44 27.23
HV-VV 99.45 3.40 2.44 29.05 8.70 3.83 73.16 0.94 27.62
Remote Sens. 2015, 7 7467
In Figure 12, four terrains are identified by both full-polarization and HH-VV SARs. HH-HV and
HV-VV SARs cannot obtain the correct scattering mechanisms, except in the sea area.
Only the retention ratio of Z5 is lower than 50% for HH-VV in Table 9. Consequently, medium
entropy dipole scatters (blue) of the mountain, forest, and building areas are set to other mechanisms in
Figure 12b. The retention ratios of the seven other zones are higher than 50%. Therefore, Figure 12b is
similar to Figure 12a.
There are six zones with retention ratios of less than 50% for HH-HV and HV-VV SARs, and five
retention ratios are less than 10%. The retention ratios of Z1 and Z8 exceed 50%; thus, low entropy
surface scattering of the sea area and high entropy dipole scattering of the mountain and forest areas are
preserved in Figure 12c,d. However, many scatters of the building area are labeled as low entropy surface
scattering. This observation indicates that the building and sea areas are confused. Furthermore, marking
most scatters of the mountain and forest areas as high entropy dipole scattering prevents the two terrains
from being differentiated. Thus, the scattering mechanisms of the mountain, forest, and building areas
in Figure 12c,d are considerably different from those in Figure 12a.
Mile Rock, Alcatraz Island, and the Golden Gate Bridge remain marked by A, B, and C in Figure 12a.
More detailed images of these areas are provided below. The scattering mechanism extraction
performance of HH-VV SAR for Mile Rock, Alcatraz Island, and the Golden Gate Bridge is close to
that of fully polarimetric SAR. The performance of HH-HV and HV-VV SARs for extracting scattering
mechanisms for the three targets is considerably worse. Low and medium entropy multiple scatters of
Alcatraz Island and the Golden Gate Bridge are not adequately discriminated; moreover, the three-parallel
scatter of the Golden Gate Bridge is converted into one- or two-parallel scatter in Figure 12c,d, respectively.
Two clear differences in the scattering mechanism extraction for Mile Rock and the Golden Gate
Bridge can be noted when comparing Figure 12 with Figure 9.
First, the scattering mechanisms of Mile Rock are low and medium entropy multiple scattering and
medium entropy surface and dipole scattering in Figure 9a,b. The multiple scattering is from the
lighthouse body and the dihedral formed by the body and base. However, only medium entropy surface
scattering is observed for Mile Rock in Figure 12a,b, with no multiple scattering being extracted, even
in several further experiments using different window sizes. This may be due to the imaging geometry.
Second, the Golden Gate Bridge appears as a thick line including low and medium entropy multiple
scattering and medium entropy surface and dipole scattering in Figure 9a because the SAR sensor
illuminated from the top of the image. Nevertheless, the bridge consists of three parallels in Figure 12a
due to the sensor illuminating from the left of the image. The left parallel is from the bridge body, with
dominant medium entropy multiple and dipole scattering and lower low entropy multiple and medium
entropy surface scattering. The middle parallel is from the cables and bridge body, with only low and
medium entropy multiple scattering. The right parallel is triple scattering from the bridge body and the
sea with low α, including medium entropy surface and dipole scattering.
6. Conclusions
The modified Cloude-Pottier decomposition is used to analyze the performance of HH-VV, HH-HV,
and HV-VV SARs for scattering mechanism extraction. We draw the following conclusions based on
the theoretical and experimental results:
Remote Sens. 2015, 7 7468
(1) HH-VV SAR can discriminate scattering from an isotropic surface, horizontal dipole, and
isotropic dihedral. Scatters diffuse to a small extent in the HH-VV H-α plane. Therefore, HH-VV
SAR extracts the eight scattering mechanisms in the H-α plane with acceptable performance.
Thus, HH-VV SAR is an alternative to fully polarimetric SAR. The average scattering mechanism
retention ratios of the three images are higher than 67%. The decreased performance of HH-VV
SAR for scattering mechanism extraction compared with that of full polarization is due to the
lack of cross-polarization.
(2) HH-HV and HV-VV SARs cannot separate surface, dipole, and multiple scattering mechanisms
because of a lack of co-polarization. The distribution of scatters in the HH-HV and HV-VV H-α
planes is quite different from that in the full-polarization H-α plan due to the scatters of most
zones strongly diffusing and transferring in the HH-HV and HV-VV H-α planes. Thus, HH-HV
and HV-VV SARs do not adequately extract scattering mechanisms in the H-α plane, indicating
that co-polarization is vital for extracting scattering mechanisms.
This paper explores the performance of dual-polarization SARs for extracting scattering mechanisms.
The performance is compared with that of fully polarimetric SAR. Comparison with compact SAR will
be performed in the next investigation.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (NSFC, No. 61372163
and 61331015). The authors would like to thank the services of the NASA/JPL, DLR, and CSA-MDA
for making the polarimetric SAR data available, and the reviewers for their valuable comments and
suggestions that significantly improved this paper.
Author Contributions
Kefeng Ji conceived and designed the experiments. Yonghui Wu performed the experiments.
Kefeng Ji and Yonghui Wu analyzed the experimental results and wrote the paper.
Conflicts of Interest
The authors declare no conflict of interest.
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... Other studies developed pseudo scattering type descriptors derived from ground range detected (GRD) Sentinel-1 products (Bhogapurapu et al., 2021) or dual-polarimetric decompositions of Sentinel-1 slant range complex (SLC) products (Haldar et al., 2021;Lu et al., 2021;Roda Husman et al., 2021). However, most studies agree that the information content of dual-polarimetric systems is only a fraction of the one which is achievable by quad-pol configurations, especially because it only contains diagonal matrix elements (Nasirzadehdizaji et al., 2019) and cannot provide the finescaled shades of entropy (Dhar et al., 2011;Ji and Wu, 2015;Xie et al., 2015). ...
... Secondly, the eigenvalues of the covariance matrix (L1, L2, L3) were calculated to extract Entropy (H; degree of randomness of targets), Anisotropy (A; impact of secondary scattering mechanism), and the average Alpha angle (α) (Cloude and Pottier, 1996). The same was done for the dual-pol products as proposed by Ji and Wu (2015) for reasons of comparison, although they underline that its application on cross-polarized data, such as Sentinel-1, is of limited quality because of the lack of co-polarization elements. To furthermore increase the polarimetric feature space, different mathematical derivates were calculated, such as the co-pol ratio (HH/VV) and cross-pol-ratio (HH/HV and VV/VH), the span as the summation of the three polarimetric intensity channels (Yahia et al., 2022), the pedestal height as the ratio between minimum and maximum eigenvalue (van Zyl et al., 1987), the Biomass Index (BMI; average copolarization backscatter intensity), and the Radar Vegetation Index by Kim and van Zyl (2001). ...
... This is furthermore underlined by the scatter plot between these features in Figure 4. Technically, they originate from the same data, but their differences arise from both resampling of the pixels of the reference product during the coregistration (Section 2.1) and the phase correction described in Section 2.1. Figure 5 shows how well Entropy, Anisotropy and Alpha derived from the pseudo-polarimetric product correlate with those extracted from the dual-polarization data of Sentinel-1A (only VV and VH) as suggested by Ji and Wu (2015). Their correlation measures are confirmed by the scatter plot: The coefficient of determination of R 2 = 0.36 states that 36% of the variation observed in the pseudo-polarimetric Entropy (blue, τ = 0.588) can be explained by the entropy derived from the dual-polarization product of Sentinel-1A. ...
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This work presents a technique to merge two Sentinel-1 image products of complementary polarimetric information (HH/HV and VH/VV) to derive pseudo-polarimetric features, such as polarimetric covariance, but also model-based and eigenvalue-based decompositions and an unsupervised Wishart classification of scattering types. The images were acquired within a 6-day period over Southern Germany and have been processed to mimic an actual quad-pol product. This was analyzed statistically, visually and within several classification processes to get an understanding of how well such a dataset depicts scattering mechanisms and other polarimetric features as inputs for land use and land cover mapping. A systematic comparison with the original dual-polarization product showed an increase in information content and largely feasible polarimetric features. Yet, especially the average Alpha angle was found to be biased and too high for some of the compared surfaces. Despite these inaccuracies, the polarimetric features turned out to improve potential land cover mapping as compared with backscatter intensities and dual-polarization features of the input products alone. Among the most significant variables related to land use and cover reported by an independent dataset, Entropy, the co-polarization ratio and the C22 element of the covariance matrix generated the strongest impact on the class separability, although misclassifications between physically related classes remain. Yet, the findings are encouraging concerning further investigation of the polarimetric potential to combine repeat-pass acquisitions of Sentinel-1 for a better description of more specific types of land cover.
... The scattering mechanism classification result can be obtained via the complex Wishart classifier proposed in Jong-Sen Lee et al. (1999). Afterwards, the Cloude-Pottier decomposition model has been improved for dual-polarized SAR images Ji and Wu (2015). In this paper, we employ the Cloude-Pottier decomposition for both full-and HH/HV dualpol SAR data Cloude et al. (1997); Ji and Wu (2015), and S(x 0 , y 0 ) Cloude et al. (1997) to demonstrate the scattering mechanisms for full-polarized SAR data. ...
... Afterwards, the Cloude-Pottier decomposition model has been improved for dual-polarized SAR images Ji and Wu (2015). In this paper, we employ the Cloude-Pottier decomposition for both full-and HH/HV dualpol SAR data Cloude et al. (1997); Ji and Wu (2015), and S(x 0 , y 0 ) Cloude et al. (1997) to demonstrate the scattering mechanisms for full-polarized SAR data. (b) indicates the time-frequency analysis model in HDEC-TFA method Huang et al. (2021a) where the backscattering variations in different range and azimuth bandwidths of SAR targets are characterized. ...
... As introduced in Section 2, the physics-based H/ -Wishart Cloude et al. (1997); Ji and Wu (2015) and HDEC-TFA Huang et al. (2021a) models serving as a part of XM, are adopted to obtain the scattering mechanism of target in SAR image , denoted as ( ). The discrete physical scattering labels ( ) either depict different zones in H/ plane Cloude et al. (1997); Ji and Wu (2015), or refer to different targets with diverse scattering variation patterns ( Fig. 2 Huang et al. (2021a). ...
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Integrating the special electromagnetic characteristics of Synthetic Aperture Radar (SAR) in deep neural networks is essential in order to enhance the explainability and physics awareness of deep learning. In this paper, we first propose a novel physically explainable convolutional neural network for SAR image classification, namely physics guided and injected learning (PGIL). It comprises three parts: (1) explainable models (XM) to provide prior physics knowledge, (2) physics guided network (PGN) to encode the knowledge into physics-aware features, and (3) physics injected network (PIN) to adaptively introduce the physics-aware features into classification pipeline for label prediction. A hybrid Image-Physics SAR dataset format is proposed for evaluation, with both Sentinel-1 and Gaofen-3 SAR data being experimented. The results show that the proposed PGIL substantially improve the classification performance in case of limited labeled data compared with the counterpart data-driven CNN and other pre-training methods. Additionally, the physics explanations are discussed to indicate the interpretability and the physical consistency preserved in the predictions. We deem the proposed method would promote the development of physically explainable deep learning in SAR image interpretation field.
... In the dual-polarization SAR system of Sentinel-1A, under the reciprocity principle, the Sinclair matrix [S d ], scattering vector k d , and coherency matrix [T d ] all differ from those of full-polarization [65]: ...
... α is the mean scattering angle (alpha angle) calculated by the weighted average of eigenvectors, with values of 0, π/4, and π/2, representing single-bounce scattering, volume scattering, and double-bounce scattering, respectively. More details on the dual-polarization H/alpha decomposition can be found in [64][65][66][67][68][69]. ...
... There must be coherent polarimetric radars; otherwise, it is not possible to calculate the off-diagonal elements of the coherency matrix. Moreover, since the scattering matrix of dual-polarization is not complete, the random surface scattering and volume scattering information extracted from a dual-polarization SAR system are limited owing to the absence of cross-polarization and overlap among various scattering mechanisms in the entropy/alpha plane [65]. Therefore, the roughness and moisture effects cannot be separated as easily as in full-polarization. ...
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Microwave remote sensing is one of the main approaches to glacier monitoring. This paper provides a comparative analysis of how different types of radar information differ in identifying debris-covered alpine glaciers using machine learning algorithms. Based on Sentinel-1A data, three data suites were designed: A backscattering coefficient (BC)-based data suite, a polarization decomposition parameter (PDP)-based data suite, and an interference coherence coefficient (ICC)-based data suite. Four glaciers with very different orientations in different climatic zones of the Tibetan Plateau were selected and classified using an integrated machine learning classification approach. The results showed that: (1) The boosted trees and subspace k-nearest neighbor algorithms were optimal and robust; and (2) the PDP suite (63.41–99.57%) and BC suite (55.85–99.94%) both had good recognition accuracy for all glaciers; notably, the PDP suite exhibited better rock and debris recognition accuracy. We also analyzed the influence of the distribution of glacier surface aspect on the classification accuracy and found that the more asymmetric it was about the sensor orbital plane, the more difficult it was for the BC and PDP suites to recognize the glacier, and a large slope could further reduce the accuracy. Our results suggested that during the inventory or classification of large-scale debris-covered alpine glaciers, priority should be given to polarization decomposition features and elevation information, and it is best to divide the glaciers into multiple subregions based on the spatial relationship between glacier surface aspect and radar beams.
... To obtain the polarization parameters, namely, the entropy (H), scattering angle (α), and anisotropy (A), this paper mainly employs H-α dual-polarization decomposition. Initially, polarization decomposition was designed for fully polarized data (RADARSAT) [24], whereas Sentinel-1 data provide only dual-polarized information, so the extraction method needs to be modified. The concept of polarization decomposition is based on the complex scattering matrix [S] (where Sfull indicates a fully polarized scattering matrix and Sdual indicates a dual-polarized scattering matrix), and for Sentinel-1, a correction needs to TSF_Jan means that data measured in January are fitted, where Jan denotes January; TSF_Feb-Apr means that data measured in February, March, and April are fitted (the river ice thickness is 0 in April in the Babao River); and in scheme 3, A_F 30-33 • , A_F 40-44 • , and D_F 40-42 • are the Babao River fitting equations, and A_F 40-45 • , D_F 30-33 • , and D_F 38-43 • are the Binggou River fitting equations (for example, in A_F 30-33 • , A means ascending orbit, D means descending orbit, F denotes fitting, and 30-33 • is the radar image incidence angle range). ...
... To obtain the polarization parameters, namely, the entropy (H), scattering angle (α), and anisotropy (A), this paper mainly employs H-α dual-polarization decomposition. Initially, polarization decomposition was designed for fully polarized data (RADARSAT) [24], whereas Sentinel-1 data provide only dual-polarized information, so the extraction method needs to be modified. The concept of polarization decomposition is based on the complex scattering matrix [S] (where S full indicates a fully polarized scattering matrix and S dual indicates a dual-polarized scattering matrix), and for Sentinel-1, a correction needs to be applied to the expression of its scattering vector [25,26], that is, to transform S full into S dual (Equations (3) and (4)): ...
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River ice on the Tibetan Plateau has important impacts on the ecosystem and hydrology. High-resolution Synthetic Aperture Radar (SAR) is an important tool for monitoring the thickness of river ice in high-altitude areas without ground data. However, due to the complex topography and narrow width, it remains challenging to monitor the ice thickness of high-order rivers (high-level branches in the plateau river system) on the Tibetan Plateau using SAR. Therefore, this paper focuses on inverting the ice thickness by utilizing dual-polarized C-band radar data. We select a typical watershed in the northeastern Tibetan Plateau, namely, the Babao River basin (including the Babao River and Binggou River), as the study area. The results show the following: (1) Dual-polarized C-band radar data have the potential to monitor the ice thickness of high-order rivers. The RMSEs of the Babao and Binggou Rivers are 0.109 m and 0.258 m, respectively. (2) Ascending and descending orbit radar images perform differently in retrieving the ice thicknesses of rivers with different directions. (3) The thickness of river ice affects the inversion accuracy. (4) Polarization parameters have varying explanatory capacities depending on the river characteristics. Our findings can provide a reference for the subsequent development of highly generalizable river ice inversion equations using dual-polarized radar data.
... This may be, in part, because we performed polarimetric decompositions on Sentinel-1 dual-pol imagery with VV and VH channels only, as opposed to quad-pol imagery. Previous work demonstrated that alpha, entropy, and anisotropy estimated winter wheat biomass moderately well (R 2 = 0.51, 0.42, and 0.44, respectively) using RADARSAT-2 quad-pol imagery, which more effectively resolves target-scattering mechanisms when compared to dual-pol SAR imagery [83]. Despite the noted model improvements in wheat and triticale biomass predictive models with the inclusion of entropy and anisotropy in this study, we observed no substantial differences when compared to the model with only InSAR coherence and NDVI_RE1 for both wheat (∆R 2 = 0; ∆RMSE = +3 kg ha −1 ; ∆MAE = −15 kg ha −1 ) and triticale (∆R 2 = 0%; ∆RMSE = +2 kg ha −1 ; ∆MAE = +2 kg ha −1 ) during cross-validation. ...
... Future work could investigate the efficacy of cover crop biomass estimations using the quad-pol polarimetric decompositions applied to imagery acquired from satellites such as RADARSAT-2, although the data are not publicly available as with Sentinel-1. Improvements in polarimetric decompositions could also be achieved by using dual-pol imagery with both linear co-polarizations (HH and VV) [83]. The compact polarimetry operating modes of RADARSAT-2 and the RADARSAT Constellation Mission (RCM)-with a circular polarization transmitted signal and V and H linear receivers-would likely lead to substantial improvements in the accuracy of polarimetric decomposition parameters compared to linear dual-pol operating modes. ...
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The magnitude of ecosystem services provided by winter cover crops is linked to their performance (i.e., biomass associated nitrogen content, forage quality, and fractional ground cover), although few studies quantify these characteristics across the landscape. Remote sensing can produce landscape-level assessments of cover crop performance. However, commonly employed optical vegetation indices (VI) saturate, limiting their ability to measure high-biomass cover crops. Contemporary VIs that employ red-edge bands have been shown to be more robust to saturation issues. Additionally, synthetic aperture radar (SAR) data have been effective at estimating crop biophysical characteristics, although this has not been demonstrated on winter cover crops. We assessed the integration of optical (Sentinel-2) and SAR (Sentinel-1) imagery to estimate winter cover crops biomass across 27 fields over three winter–spring seasons (2018–2021) in Maryland. We used log-linear models to predict cover crop biomass as a function of 27 VIs and eight SAR metrics. Our results suggest that the integration of the normalized difference red-edge vegetation index (NDVI_RE1; employing Sentinel-2 bands 5 and 8A), combined with SAR interferometric (InSAR) coherence, best estimated the biomass of cereal grass cover crops. However, these results were season- and species-specific (R2 = 0.74, 0.81, and 0.34; RMSE = 1227, 793, and 776 kg ha−1, for wheat (Triticum aestivum L.), triticale (Triticale hexaploide L.), and cereal rye (Secale cereale), respectively, in spring (March–May)). Compared to the optical-only model, InSAR coherence improved biomass estimations by 4% in wheat, 5% in triticale, and by 11% in cereal rye. Both optical-only and optical-SAR biomass prediction models exhibited saturation occurring at ~1900 kg ha−1; thus, more work is needed to enable accurate biomass estimations past the point of saturation. To address this continued concern, future work could consider the use of weather and climate variables, machine learning models, the integration of proximal sensing and satellite observations, and/or the integration of process-based crop-soil simulation models and remote sensing observations.
... Temporal change in H-α plane ( Figure.4) is evaluated to discriminate the crops in the same proximity, but due to similar alpha angle values it is not capable of separating the crop types with different entropy values and scattering mechanisms [6]. Moreover, it is not synchronous to the zones derived for quad-pol data which helps in discriminating different land features based on the assigned zones for different scattering mechanisms due to lower alpha angle values which are possibly due to cross polarization and dual-pol data [10]. ...
Conference Paper
Synthetic Aperture Radar (SAR) data have been proven useful for agricultural monitoring and crop discrimination. The current study focused on sensitivity analysis of cotton and groundnut crop biophysical parameters and polarimetric parameters evaluated from dual polarized (VV-VH) Sentinel-1 SAR temporal datasets. Simple linear and logarithmic regression with Leaf Area Index (LAI) and plant height respectively gives reasonable correlation with Radar Vegetation Index (RVI) and Entropy (H), Anisotropy (A) and Alpha (α) decomposition. RVI is well correlated with LAI and plant height (R² = 0.83) for both the crops. For H-A-α decomposition, entropy has maximum correlation with plant height (R² = 0.43) for cotton and LAI (R² = 0.49) for groundnut. Alpha angle values are observed to be similar for both the crops which make it difficult to discriminate them in H-α plane. Dual-pol Sentinel-1 SAR can be potentially utilized for evaluating crop biophysical parameters in its temporal variation.
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Mapping and monitoring changes in the distribution of cropland provides information that aids sustainable approaches to agriculture and supports early warning of threats to global and regional food security. Data from synthetic aperture radar (SAR) sensors can make an important contribution to these crop monitoring activities. This study tested the capability of PALSAR multi-polarization and polarimetric data for crop classification. L-Band results were compared with those achieved with a C-Band SAR data set (ASAR and RADARSAT-1), an integrated C- and L-Band data set, and a multi-temporal optical data set (Landsat Thematic Mapper). Using all L-Band linear polarizations corn, soybeans, cereals and hay-pasture were classified to an overall accuracy of 70%. A more temporally-rich C-Band data set provided an accuracy of 80%. Larger biomass crops (corn and soybeans) were well classified using the PALSAR data. C-Band data were needed to accurately classify low biomass crops (cereals and hay-pasture). With a multi-frequency data set an overall accuracy of 88.7% was reached, and many individual crops were classified to accuracies better than 90%. These results were competitive with the overall accuracy achieved using three Landsat images (88.0%). L-Band parameters derived from three decomposition approaches (Cloude-Pottier, Freeman-Durden and Krogager) produced superior crop classification accuracies relative to those achieved using the linear polarizations. Using the Krogager decomposition parameters from all three PALSAR acquisitions, an overall accuracy of 77.2% was achieved. Results reported in this study emphasize the value of polarimetric as well as multi-frequency SAR data for crop classification. With such a diverse capability, a SAR-only approach to crop classification becomes increasingly viable. Access to multi-polarization data from both RADARSAT-2 and TerraSAR-X promises to further advance the use of SAR for agricultural applications.
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The monitoring of soil freezing and thawing states over large areas is very challenging on ground. In order to investigate the potential and the limitations of space-borne SAR polarimetry at C-band for soil state survey, analyses were conducted on an entire winter time series of fully polarimetric RADARSAT-2 data from 2011/2012 to identify freezing as well as thawing states within the soil. The polarimetric data were acquired over the Sodankyla test site in Finland together with in situ measurements of the soil and the snow cover. The analyses indicate clearly that the dynamics of the polarimetric entropy and mean scattering alpha angle are directly correlated to soil freezing and thawing states, even under distinct dry snow cover. First modeling attempts using the Extended Bragg soil scattering model justify the observed trends, which indicate surface-like scattering during frozen soil conditions and multiple/volume scattering for thawed soils. Hence, these first investigations at C-band foster motivation to work towards a robust polarimetric detection of soil freezing and thawing states as well as their transition phase.
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The recent launches of three fully polarimetric synthetic aperture radar (PolSAR) satellites have shown that polarimetric radar imaging can provide abundant data on the Earth’s environment, such as biomass and forest height estimation, snow cover mapping, glacier monitoring, and damage assessment. Written by two of the most recognized leaders in this field, Polarimetric Radar Imaging: From Basics to Applications presents polarimetric radar imaging and processing techniques and shows how to develop remote sensing applications using PolSAR imaging radar. The book provides a substantial and balanced introduction to the basic theory and advanced concepts of polarimetric scattering mechanisms, speckle statistics and speckle filtering, polarimetric information analysis and extraction techniques, and applications typical to radar polarimetric remote sensing. It explains the importance of wave polarization theory and the speckle phenomenon in the information retrieval problem of microwave imaging and inverse scattering. The authors demonstrate how to devise intelligent information extraction algorithms for remote sensing applications. They also describe more advanced polarimetric analysis techniques for polarimetric target decompositions, polarization orientation effects, polarimetric scattering modeling, speckle filtering, terrain and forest classification, manmade target analysis, and PolSAR interferometry. With sample PolSAR data sets and software available for download, this self-contained, hands-on book encourages you to analyze space-borne and airborne PolSAR and polarimetric interferometric SAR (Pol-InSAR) data and then develop applications using this data.
Article
Classification, decomposition and modeling of polarimetric SAR data has received a great deal of attention in the recent literature. The objective behind these efforts is to better understand the scattering mechanisms which give rise to the polarimetric signatures seen in SAR image data. In this paper, a new approach is described, which involves the fit of a combination of three simple scattering mechanisms to the polarimetric SAR observations. The mechanisms are volume scatter from a cloud of randomly oriented dipoles, even-bounce scatter from a pair of orthogonal surfaces with different dielectric constants and Bragg scatter from a moderately rough surface. This composite scattering model is used to describe the polarimetric backscatter from naturally occurring scatterers. Results are presented of application of this new algorithm to different types of scene, including multi-frequency polarimetric SAR images of a tropical rain forest, a boreal forest, a pine forest, geologic targets, urban areas and agricultural fields. Fitting the model to polarimetric SAR data of the tropical rain forest for example, allows clear discrimination between flooded and non-flooded forest. The model can be used to estimate the overall contribution from each of the three basic scattering mechanisms for each SAR image pixel.
Article
This study focuses on the application of H/α decomposition to original compact polarimetric (CP) synthetic aperture radar (SAR) data. In general, the authors can extract the physical scattering mechanisms (PSMs) of targets by using pseudo fully polarimetric (FP) data that are approximately reconstructed from the original CP data. In this study, the H/α decomposition is extended to the original CP data to avoid large data volume and heavy computational burden during the reconstruction of pseudo FP data, while escaping from the possible information loss caused by the reconstruction process. The H/α plane is modified and re-plotted out to discriminate different PSMs from CP data. Two CP modes are considered in the study: the α/4 mode and the dual circular polarimetric (DCP) mode. The study shows that under the DCP mode, the modified H/α decomposition performs well to discriminate different PSMs, whereas it collapses in the α/4 mode. The feasibility and effectiveness of the new H/α decomposition for CP modes are analysed and verified by experiments with measured airborne data.
Article
The feasibility of retrieving the phenological stage of rice fields at a particular date by employing coherent copolar dual-pol X-band radar images acquired by the TerraSAR-X sensor has been investigated in this paper. A set of polarimetric observables that can be derived from this data type has been studied by using a time series of images gathered during the whole cultivation period of rice. Among the analyzed parameters, besides backscattering coefficients and ratios, we have observed clear signatures in the correlation (in magnitude and phase) between channels in both the linear and Pauli bases, as well as in parameters provided by target decomposition techniques, like entropy and alpha from the eigenvector decomposition. A new model-based decomposition providing estimates of a random volume component plus a polarized contribution has been proposed and employed in interpreting the radar response of rice. By exploiting the signatures of these observables in terms of the phenology of rice, a simple approach to estimate the phenological stage from a single pass has been devised. This approach has been tested with the available data acquired over a site in Spain, where rice is cultivated, ensuring ground is flooded for the whole cultivation cycle, and sowing is carried out by randomly spreading the seeds on the flooded ground. Results are in good agreement with the available ground measurements despite some limitations that exist due to the reduced swath coverage of the dual-pol HHVV mode and the high noise floor of the TerraSAR-X system.
Article
In this paper we develop a dual polarized version of the entropy/alpha decomposition method. We first develop the basic algorithms and then apply them to theoretical models of surface and volume scattering to demonstrate the potential for discrimination, classification and parameter estimation. We then apply the formalism to d ual polarized data from the ALOS/PALSAR system operating in PLR and FBD modes to illustrate application to forest classification, urban scattering characterization and point target signature analysis for ship classification.