Compact polarimetry

1. Journal of Systems Engineering and Electronics
Vol. 25, No. 3, June 2014, pp.1–9
Multi-polarization reconstruction from compact polarimetry
based on modified four-component scattering decomposition
Junjun Yin∗ and Jian Yang
Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
Abstract: An improved algorithm for multi-polarization reconstruc-tion
from compact polarimetry (CP) is proposed in this paper. Ac-cording
to two fundamental assumptions in compact polarimetric
reconstruction, two improvements are proposed. Firstly, the four-component
model-based decomposition algorithm is modified with
a new volume scattering model. The decomposed helix scattering
component is then used to deal with the non-reflection symmetry
condition in compact polarimetric measurements. Using the de-composed
power and considering scattering mechanism of each
component, an average relationship between the co-polarized and
cross-polarized channels is developed over the original polariza-tion
state extrapolation model. E-SAR polarimetric data acquired
over the Oberpfaffenhofen area and JPL/AIRSAR polarimetric data
acquired over San Francisco are used for verification and good re-construction
results are obtained, demonstrating the effectiveness
of the proposed method.
Keywords: polarimetric synthetic aperture radar (SAR), target
decomposition, compact polarimetry (CP), multi-polarization re-construction.
DOI: 10.1109/JSEE.2014.000
1. Introduction
The polarimetric synthetic aperture radar (PolSAR) has
been widely used in many earth observing applications,
such as terrain classification [1–4], land cover monitoring
[5–7], and targets detection [8–10]. The space-borne fully
polarimetric SAR sensor has many advantages. However,
it suffers from increment of the pulse repetition frequency,
the power consumption, and the downloading data rate. In
addition, the imaging coverage of full polarimetry is only
half the width of a single-polarized or dual-polarized sys-tem.
The dual polarization SAR system is a compromising
choice between full polarization and single polarization. A
Manuscript received October 19, 2012.
*Corresponding author.
This work was supported by the National Natural Science Foundation
of China (41171317), the State Key Program of the Natural Science Foun-dation
of China (61132008), and the Research Foundation of Tsinghua
University.
dual-polarized SAR, which transmits a single polariza-tion
and receives two orthogonal polarizations, does not
provide complete information of targets pertaining to the
quadrature polarization states, but it offers more informa-tion
than a single-polarized system [11,12].
In order to obtain more information from the dual polar-ization,
Souyris et al. proposed a dual polarization imag-ing
mode, i.e., compact polarimetry (CP) [12–15], based
on one unique special transmitted polarization and two or-thogonal
polarizations in reception. There are mainly two
ways to cope with the CP measurements. One is to use CP
data directly without any assumptions; the other is to re-construct
the multi-channel polarimetric information over
extended/distributed targets from the CP design. In the
multi-polarization reconstruction procedure, two assump-tions
are very essential. One is the well-known reflection
symmetry assumption, and the other is the polarization
state extrapolation model. With both the assumptions, an
iterative process was introduced by Souyris et al., and the
reconstructed polarimetric data performed well to a certain
degree [12–15].
However, the reflection symmetry is not always valid
especially in urban areas, where the reconstructed results
are always far from the actual values. In order to derive
more target information from CP and accommodate the
fully polarimetric (FP) information reconstruction scheme
with the more general scattering cases, an improved polari-metric
information reconstruction algorithm is proposed
in this paper. This algorithm is based on modified four-component
decomposition with a new volume scattering
model. By assuming a coherency matrix is totally decom-posed
into four individual components, an average extrap-olated
model relating to the different scattering mecha-nisms
is proposed. Using the proposed reconstruction al-gorithm,
the helix scattering power can be estimated from
the 2 × 2 CP covariance matrix.
The outline of this paper is given as follows. A brief

2. 2 Journal of Systems Engineering and Electronics Vol. 25, No. 3, June 2014
overview of the four-component decomposition [16] and
the modified decomposition method are summarized in
Section 2. In Section 3, the linear π/4 compact polarimet-ric
mode is briefly described, and then a multi-polarization
reconstruction algorithm is proposed. Two sets of polari-metric
SAR (PolSAR) data are used for demonstrating the
effectiveness of the proposed reconstruction method. The
corresponding experimental results and analysis are pre-sented
in Section 4. Section 5 draws the conclusions.
2. Modified four-component model
decomposition
In a linear horizontal (H) and vertical (V) polarization base,
the Pauli target scattering vector is defined as follows under
the reciprocity principle for the monostatic backscattering
case.
kp =
√1
2
[SHH + SVV SHH − SVV 2SHV]T (1)
where SHV is the backscattered coefficient by V in trans-mission
and H in reception. In themulti-look case, the scat-tering
coherency matrix T is usually used to deal with
statistical scattering effects. T given in the following is a
non-negative definite Hermitian matrix.
T = kpkH
p
(2)
where · denotes the ensemble averaging, and the super-script
H denotes the conjugate transpose.
2.1 Four-component decomposition
The Yamaguchi four-component decomposition models
the coherency/covariance matrix as the contribution of
four scattering mechanisms, i.e., the surface scattering, the
double-bounce scattering, the volume scattering, and the
helix scattering [16].
T = fs · Ts + fd · Td + fv · Tv + fc · Tc (3)
where fs, fd, fv, and fc correspond to the coefficients
of the four scattering components, which are non-negative
and proportional to their powers, Ts, Td, and Tc denote the
surface scattering, the double-bounce scattering, and the
helix scattering models, respectively, and they are modeled
as follows based on different physical scattering mecha-nisms.
Ts =
⎡
⎣
1 β∗ 0
β |β|2 0
0 0 0
⎤
⎦, Tc =
⎡
⎣
0 0 0
0 1 ±j
0 ∓j 1
⎤
⎦,
Td =
⎡
⎣
|α|2 α 0
α∗ 1 0
0 0 0
⎤
⎦ (4)
where α and β are unknown parameters to be de-termined.
There are three volume scattering models
for Tv, and the choice is based on the value of
10 lg(|SVV|2/|SHH|2). Please refer to [16] for more de-tails.
When the original four-component decomposition is ap-plied
to the real PolSAR data, some scattering component
powers may become negative. To overcome this problem,
an improved decomposition is proposed with a power con-straint
[17]. The basic principle is that if the decomposed
power becomes negative, then the power is forced to zero
and let the sum of the decomposed powers be equal to
span.
span =
1
2
|SHH + SVV|2+
1
2
|SHH − SVV|2 + 2|SHV|2
(5)
where span is the Frobenius norm of the scattering vec-tor.
Four-component decomposition has been successfully
applied to analyze the PolSAR data, especially for the area
with man-made targets (e.g., the urban area) where the re-flection
symmetry condition does not hold.
2.2 Volume scattering model
The volume scattering can be regarded as an ensemble av-eraging
of chaotic scattering states, and cannot be char-acterized
as a deterministic scattering process. Instead of
the original three volume models in [16], a special volume
scattering model [18] Tvol is adopted in this paper.
T
vol =
⎡
⎣
1 0 0
0 1 0
0 0 1
⎤
⎦. (6)
There are three reasons for us to choose this model for
FP information reconstruction. First, it follows from the
fully depolarized wave assumption. This model satisfies
the polarization state extrapolation model [12] which is
related to the intensity ratio between cross-polarized and
co-polarized channels and the linear co-polarization cohe-rence
|ρ|.⎧⎪⎨
⎪⎩
|SHV|2
|SHH|2 + |SVV|2 =
1
4
(1 − |ρ|)
ρ = SHHS
∗
VV
/
|SHH|2|SVV|2
. (7)
This model is extrapolated from the case where the
backscattered wave is either fully polarized or fully de-polarized.
For a fully polarized backscattered wave from
a simple point target, |ρ| ≈ 1; for a fully depolarized
backscattered wave, which means that the co-polarized
channels are almost completely uncorrelated, and the
average power received by the orthogonal antennas do
not depend on their polarization states, |ρ| ≈ 0 and

3. Junjun Yin et al.: Multi-polarization reconstruction from compact polarimetry based on modified four-component scattering... 3
|SHH|2 ≈ |SVV|2 ≈ 2 |SHV|2 . Tak-ing
the Freeman volume scattering model [19] for exam-ple,
we have |SHV|2/(|SHH|2 + |SVV|2) = 1/6 and
|ρ| = 1/3. Though both the values follow from the factor
1/4 in (7), the co-polarization coherence |ρ|= 0, which
is not consistent with the fully depolarized backscatter-ing
case [14, 15]. Using the volume scattering model in
(6), we have |SHV|2/(|SHH|2 + |SVV|2) = 1/4 and
|ρ| = 0. Both the values are consistent with the relation-ship
model in (7) and the fully depolarized backscattering
wave assumption.
The second reason is that Tvol has the maximum polari-metric
entropyH.H introduced by Cloude and Pottier rep-resents
the randomness of backscattered waves. High en-tropy
circumstance often occurs in the region with highly
anisotropic scattering elements, e.g., scattering from for-est
canopies and scattering from vegetated surfaces. In ex-treme,
H = 1 denotes totally random scattering. This sit-uation
is expected to occur when a significant amount of
multiple scattering is present such as in the case of scatter-ing
from extremely rough surfaces. If some deterministic
scattering process where H = 0 is added to the model
Tvol, the backscattering will be less random, leading to
H 1. Thus, all the scattering models can be regarded as
an addition of Tvol and deterministic scattering processes,
and the balance among them determines H. Thus, Tvol is
selected as a description of ideal random scattering.
The third reason is that Tvol is an azimuthally symmet-ric
scattering model, which reduces the orientation angle
effect when the target decomposition is expanded. From
the above analysis, the model (6) is reasonably employed
for characterizing the most random scattering targets, then
a simple relationship between the helix scattering and the
volume scattering components can be obtained by using
this model. This is the basic idea of the modified four-component
decomposition. The derived relations between
different scattering models will be used for the reconstruc-tion
of pseudo FP information.
2.3 Modified four-component decomposition
From the scattering models defined in (4) and (6), the co-herency
matrix can be decomposed into four scattering
components. By comparing the measured data with both
the sides of (3), we can derive the helix scattering power
and the volume scattering power as follows:
fc = Im|(SHH − SVV)S∗
HV
|, Pc = 2fc
fv = 2|SHV|2 − fc, Pv = 3fv
(8)
where Pv and Pc denote the powers of the volume scatter-ing
and the helix scattering, respectively. The flow chart of
the whole modified four-component model-based decom-position
algorithm is given in Fig. 1, where Ps and Pd are
the decomposed powers of the surface scattering and the
double-bounce scattering components, respectively. The
foremost reason for adopting model (6) to decompose the
coherency matrix is that we can obtain a simple relation-ship
expressed in (8) to relate the elements in a 3 × 3
FP matrix to a 2 × 2 CP matrix. In the original Yam-aguchi
four-component decomposition, three volume scat-tering
models derived from different probability density
functions are used for decomposition, which leads to mul-tiple
relationships between the helix scattering component
and the volume scattering component. The point of this pa-per
is not to analyze the target scattering characteristics but
to reconstruct the FP information from the linear compact
mode. Using the new model in (6), a simpler formula (8)
is obtained to relate the helix and the volume scattering
Fig. 1 Flow chart of the modified four-component decomposition

4. 4 Journal of Systems Engineering and Electronics Vol. 25, No. 3, June 2014
components to the cross-polarized measurement
|SHV|2 . In this way, the helicity parameter fc can also
be estimated from the reconstruction procedure. Based on
the decomposed powers, an improved multi-polarization
reconstruction algorithm is presented in next section.
3. Multi-polarization reconstruction
3.1 π/4 mode compact polarimetry
The π/4 mode [12] features two linear receiving polariza-tions,
i.e., the horizontal and vertical polarizations, and
the transmitting polarization which is linear and oriented
at 45◦. The scattering vector for the π/4 mode is given by
kπ/4 =
[SHH + SHV SVV + SHV]T
√
2
. (9)
For simplicity, the constant coefficient 1/
√
2 is omitted
hereafter. Then Cπ/4 = kπ/4kH
π/4
given in (10) is the
corresponding covariance matrix, which can be regarded
as contributions of three parts, i.e., the part associated with
the co-polarized channels, the cross-polarized channel in-formation,
and the correlations between co-polarized and
cross-polarized backscattering coefficients.
Cπ/4 =

5. C11 C12
C∗
12 C22
=

6. |SHH|2 SHHS∗
VV
SVVS∗
HH
|SVV|2
+
|SHV|2

7. 1 1
1 1
+

8. 2Re(SHHS∗
HV) SHHS∗
HV + SHVS∗
VV
SHVS∗
HH + SVVS∗
HV 2Re(SVVS∗
HV)
(10)
where Cπ/4 is a semi-definite Hermitian matrix. Under
the assumption of reflection symmetry, there is a com-plete
de-correlation between the co-polarization and cross-polarization,
i.e., SHHS∗
HV
= SVVS∗
HV
= 0.
Regarding the third term in (10) as zero by assuming
the reflection symmetry, we have an underdetermined sys-tem
of three equations and four unknown variables, i.e.,
|SHH|2, |SHV|2, |SVV|2 and SHHS∗
VV
. In order to
construct the reflection symmetric fully polarimetric infor-mation,
the pseudo deterministic trend (7) is used to re-late
the four unknowns. |SHV|2 is the key parameter for
the solution and can be solved by iteration. Please refer to
[12] for more details of the Souyris’ reconstruction algo-rithm.
The iteration termination condition is that either the
co-polarized coherence is |ρ| = 1 or |SHV|2 is conver-gent.
If a converged value of |SHV|2 is obtained as X,
the reconstructed fully polarimetric covariance matrix for
extended targets is shown as follows:
Cπ/4−FP =
⎡
⎣
C11 − X 0 C12 − X
0 2X 0
C∗
12
− X 0 C22 − X
⎤
⎦. (11)
3.2 New polarization state extrapolation model
Two assumptions are introduced to perform the FP recon-struction
procedure. One is the reflection symmetry, and
the other is the polarization state model. The reflection
symmetry applies reasonably well in general analysis of
natural distributed scatterers. For urban areas, however, the
reflection symmetry does not hold because of the strong
point target reflection. In order to accommodate the recon-structed
results for more general cases and extract more
polarization information, it is necessary to consider an-other
physical scattering mechanism which corresponds to
SHHS∗
HV
= 0 and SVVS∗
HV
= 0. Therefore the modi-fied
four-component decomposition is adopted here. From
the third part of (10), we have
ImSHHS
∗
HV + S
∗
VVSHV = Im(SHH − SVV)S
∗
HV
(12)
where Im(SHH − SVV)S∗
HV
is the helix scattering. Let
F = Im(SHHS∗
HV + SHVS∗
VV). The covariance matrix of
the π/4 mode can be approximated by
Cπ/4
≈

9. |SHH|2 SHHS∗
VV
S∗
HHSVV |SVV|2
+|SHV|2

10. 1 1
1 1
+

11. 0 jF
−jF 0
. (13)
Next we consider the polarization state model. Consi-dering
the helix scattering component, we propose an im-proved
relationship based on the modified four-component
decomposition, which assumes that the coherency matrix
of a pixel is totally contributed by four scattering compo-nents.
Thus, we establish an average model with conside-ring
each separate scattering mechanism.
First we calculate |SHV|2/(|SHH|2 + |SVV|2) and
|ρ| according to (4) and (6), respectively. For the surface
scattering and the double-bounce scattering models, we
have
|SHV|2
|SHH|2 + |SVV|2 = 0, |ρ| = 1. (14)
Following van Zyl [20], we decide the co-polarized co-herence
coefficient ρ is equal to 1 for the surface scat-tering,
which means the resulting backscattered waves of
SHH and SVV are in phase, and we decide ρ is equal to
−1 for the double-bounce scattering, which means that

12. Junjun Yin et al.: Multi-polarization reconstruction from compact polarimetry based on modified four-component scattering... 5
the co-polarized phase difference will in general be nearly
180◦. For the helix scattering model, we have
|SHV|2
|SHH|2 + |SVV|2 =
1
2, ρ= −1. (15)
The backscattered waves of these three models are fully
polarized, i.e., |ρ| = 1, which characterize deterministic
scattering processes. In the volume scattering case, the po-larization
ratio and the coherence coefficient are 1/4 and 0,
respectively. Thus the volume scattering Tvol is a fully
depolarized scattering of backscattered waves in extreme.
In order to acquire the relationship between the co-polarized
and cross-polarized channels, in [12] a more
physical model based on the polarization properties is also
investigated. Accordimg to the lightened rotation symme-try
assumption [21], we have
4|SHV|2 = |SHH|2 + |SVV|2 − 2Re(SHHS
∗
VV).
(16)
Three basic scattering mechanisms of the four mod-els
except the double-bounce scattering are consistent
with this hypothesis. However, the even number reflec-tion
is an important scattering behavior in the backscat-tering
process. Thus, reconstructed results extrapolated by
this model are not desirable. Though the relationship de-scribed
in (7) has a better result [12], it does not quite fit the
real PolSAR data especially for urban areas with complex
structures. Combining with the advantages of both models,
we propose an improved model.
By four-component decomposition, we assume that the
FP coherency matrix has been decomposed and the corre-sponding
results are Ps, Pd, Pv and Pc, respectively. Then
the average value of |SHV|2/(|SHH|2 + |SVV|2) can
be regarded as the contribution of the four components.We
have
|SHV|2
|SHH|2 + |SVV|2 =
1
4
Pv
span
+
1
2
Pc
span
. (17)
Assuming the backscattering covariance matrix is a
weighted sum of the four scattering processes, the correla-tion
coefficient ρ should be real (positive or negative) and
ρ ranges from −1 to 1. Similarly, the average value of ρ is
ρ = Ps
span
− Pd
span
− Pc
span
. (18)
(18) can be rewritten as 1−ρ=(2Pd+2Pc + Pv)/span.
For naturally distributed targets, ρ is complex. Thus, a
modified polarization relationship considering the coher-ence
coefficient phase for a more general scattering case
should be established with |ρ|. The improved model is
shown as follows:
|SHV|2
|SHH|2 + |SVV|2 =
1 − sgn(ReSHHS∗
VV
)|ρ|
4
2Pc + Pv
2Pd + 2Pc + Pv
(19)
where sgn(x) is a signum function; Re(x) denotes the
real part of x. The right-hand side of (19) resembles (7),
but with a coefficient which is less than one. From pre-vious
researches related to compact polarimetry, a phe-nomenon
observed by many researchers is that the value
of |SHV|2/(|SHH|2 + |SVV|2) is usually far smaller
than (1 − |ρ|)/4. Therefore, adding a coefficient (smaller
than 1) to the right side of (7) may produce a better re-construction
result. Using the fully polarimetric E-SAR
Oberpfaffenhofen data shown in Fig. 2, scatter plots of the
two sides of (7) and (19) are shown in Fig. 3 (a) and (b),
respectively. For a better equality, the scatter points should
lie along the diagonal line to support the validity of the po-larization
state model. However, few points fall close to the
diagonal line in Fig. 3 (a), indicating that the extrapolated
model (7) is not always valid to fit the real data, at least
for this data set. Using the proposed model, most data lie
close to the eye line in Fig. 3 (b), which is evident that (19)
shows a better fit to the real backscattering mechanisms.
Next we will present how to estimate both the values of
2Pc + Pv and 2Pd +2Pc + Pv by using a simple approxi-mation
approach based on the π/4 CP measurements.
Fig. 2 Pauli-basis image of original E-SAR Oberfaffenhofen FP
data

13. 6 Journal of Systems Engineering and Electronics Vol. 25, No. 3, June 2014
Fig. 3 Scatter distribution of the Oberfaffenhofen area
3.3 Parameter estimation
From the coherency matrices shown in (4) and (6), accor-ding
to (10), we synthesize the corresponding compact
scattering models as follows:
Cπ/4−s =

14. |β|2 β
β∗ 1
, Cπ/4−d =

15. |α|2 α
α∗ 1
Cπ/4−c =

16. 1 ±j
∓j 1
, C
π/4−v =

17. 1.5 0.5
0.5 1.5
(20)
where Cπ/4−s, Cπ/4−d, Cπ/4−c, Cπ/4−v are the covari-ance
matrices of the surface scattering, double-bounce
scattering, helix scattering, and volume scattering com-ponents,
respectively; α and β are defined after Freeman
[19]. One constraint is that the powers of mutually re-lated
components should be equal, i.e., span(Cπ/4−c) =
span(Tc) and span(C
π/4−v) = span(Tvol), which
can guarantee the decomposed powers from the CP mode
are equal to those from the FP mode measurements.
We expand the compact covariance matrix as
Cπ/4=fs·Cπ/4−s+fd·Cπ/4−d+fc·Cπ/4−c+fv·C
π/4−v
(21)
where fs, fd, fc, and fv are the expansion coefficients as
those defined in (3). Let the corresponding scattering po-wers
be Ps, Pd, Pc, and Pv, respectively. By comparing
the measured data of the two sides of (21), we have
⎧⎨
⎩
fs + fd + fc + 1.5fv = C11
|β|2fs + |α|2fd + fc + 1.5fv = C22
βfs + αfd ± jfc + 0.5fv = C12
. (22)
Since the relationship between fc and fv has been
known, as shown in (8), we have the previous three
equations with four unknowns α, β, fs, and fd, which
can be solved in a similar manner as that in [19]. If
Re(C12) is positive, we decide that the surface scatter-ing
is dominant and let α = −1. If Re(C12) is nega-tive,
we decide that the double-bounce scattering is domi-nant
and let β = 1. Finally, the surface scattering power Ps
and the double-bounce scattering power Pd can be derived
as
A =
C11 − fc − 3
2 fv
C22 − fc − 3
2 fv
−
Re(C12) − 1
2 fv
2
B = C11 + C22 − 2fc − 2fv (23) if β = 1
2A
⎩
thenPs ⎧⎨
=
B − 2real(C12)
or
⎧⎨
⎩
if α = −1
thenPd =
2A
B − 2fv + 2real(C12)
In Freeman’s decomposition, the sign of the real part of
SHHS∗
VV
is used to decide whether the double-bounce
scattering or the surface scattering is dominant. In this
study, the decision principle is replaced by Re(C12) for
the CP mode. Several fully polarimetric data sets including
the two images shown in the following experiment section
have been used to verify this decision principle. We use
Ps −Pd 0 for the FP mode and Re(C12) 0 for the CP
mode to determine the area dominated by single-bounce or
even-bounce scattering. By comparing the two determined
results, it is found that the area differentiation is no more
than 5%. Thus, this principle to decide which scattering
mechanism is predominant is valid for the CP mode. Then
the approximated values of 2Pc +Pv and 2Pd +2Pc +Pv
could be estimated and updated from the iteration process.

18. Junjun Yin et al.: Multi-polarization reconstruction from compact polarimetry based on modified four-component scattering... 7
3.4 Proposed multi-polarization reconstruction
algorithm
We also employ an iterative approach to solve the non-linear
system.
Initializations, as we can get as follows:
⎧⎪⎨
⎪⎩
fc(0) = |F(0)
| = 0
ρ(0) = √ C12
C11C22
⇒
⎧⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎩
X(0) = C11 + C22
2
1 − |ρ(0)
|
3 − |ρ(0)
|
SHHS∗
VV
(0) = ρ(0)
(C11 − X(0))(C22 − X(0))
fc(0) = |F(0)
| = |Im(C12 − SHHS∗
VV
(0))|
fv(0) = 2X − fc(0)
.
(24)
Iterations, as we can get as follows:
w =
⎧⎪⎪⎨
⎪⎪⎩
4fc + 3fv
2Pd + 4fc + 3fv
, Re(C12) 0
4fc + 3fv
2span − 3fv − 2Ps
, Re(C12) 0
ρ(i+1) =
C12 −
X(− i)
jF(i) (C11 − X(i))(C22 − X(i))
X(i+1)= C11+C22
2
(1−sgnRe(C12)|ρ(i+1)
|) · w
2 + (1 − sgnRe(C12)|ρ(i+1)
|) · w
SHHS
∗
VV
(i+1)=ρ(i+1)
(C11−X(i+1))(C22−X(i+1))
fc(i+1) = |F(i+1)
| = |Im(C12 − SHHS
∗
VV
(i+1))|
fv(i+1) = 2X(i+1)
− fc(i+1)
where X = |SHV|2, Pv = 3fv, Pc = 2fc, span =
C11 + C22, and i is the iteration number. Before tak-ing
the reconstruction procedure, we should determine
which scattering mechanism is dominant, and then se-lect
the corresponding formula in (23) to calculate the
value of Ps or Pd for iteration. Since the number of un-knowns
exceeds the number of equations, we let fc(0) =
0 at first. Then the initial value for fc(0) is updated by
the initialized |SHV|2
(0) and SHHS∗
VV
(0). The vol-ume
scattering coefficient fv is assigned by the ith
estimated |SHV|2
(i) and fc(i). Due to the violations
of the underlying assumption in iteration, |ρ|
(i) may
become larger than one, or the power of the volu-me
scattering may become negative throughout the itera-tions.
In both cases, we regularize the approximation va-lues
to be the (i − 1)th iterative results and then halt the
iteration. Suppose the nth order estimated values of Fn
and Xn are given, the reconstructed FP coherency matrix
is shown as follows:
Tπ/4−FP =
⎡
⎢⎢⎢⎢⎣
γ1 + 2Re(C12) − 4Xn
2
γ2−j2(Im(C12)−Fn)
2
0
γ2+j2(Im(C12)−Fn)
2
γ1 − 2Re(C12)
2
jFn
0 −jFn 2Xn
⎤
⎥⎥⎥⎥⎦
(26)
where γ1 = C11 + C22, γ2 = C11 − C22.
Due to the relationship between the Lexicographic target
scattering vector and the Pauli scattering vector, the unitary
transformation formula between the scattering covariance
matrix C and the scattering coherency matrix T is
Cπ/4−FP =
⎡
⎣
|SHH|2
√
2SHHS∗
HV SHHS∗
√ VV
2SHVS∗
HH 2|SHV|2
√
2SHVS∗
VV
SVVS∗
HH
√
2SVVS∗
HV
|SVV|2
⎤
⎦
=
DT
3 Tπ/4−FPD3 (27)
whereD3 =
1 √
2
⎡
⎣
1 0 1
1 √
0 −1
0
2 0
⎤
⎦.
Thus, the linear basis multi-polarization information is
reconstructed.
4. Experimental results
The proposed multi-polarization reconstruction algorithm
is applied to two PolSAR data sets. One is the E-SAR
L-band data acquired over the Oberfaffenhofen area in
Germany. The image has 1 300 pixel× 1 200 pixel. Fig. 2
is the Pauli–basis image, from which we can see several
kinds of terrain types such as airports, urban areas, farm-lands,
and forests. The other is the NASA/JPL AIRSAR L-band
data acquired over San Francisco, shown in Fig. 4. It
Fig. 4 San Francisco test area

19. 8 Journal of Systems Engineering and Electronics Vol. 25, No. 3, June 2014
has 700 pixel × 900 pixel and consists of a variety of dis-tinctive
scattering mechanisms. Both images are filtered by
a 3 × 3 average sliding window.
4.1 Reconstruction performance
First, an experiment is used to illustrate and assess the va-lidity
of the modified reconstruction algorithm. The π/4
mode compact polarimetric data are generated from the
original fully polarimetric data. Fig. 5 shows the Pauli-basis
reconstructed results by the two methods, i.e., the
Souyris’ method and the proposed method. It is clear that
both images indicate a good overall agreement with the FP
image over the whole area, but Fig. 5 (b) looks much bluer
than Fig. 5 (a) in the forest area blocked by the bold white
rectangle. This phenomenon is closer to the FP Pauli-basis
image shown in Fig. 2 and more consistent with the actual
physical scattering mechanism in forests.
Fig. 5 Pauli-basis images of the reconstructed data
Fig. 6 shows the scatter plots of the Oberpfaffenhofen
test data. Fig. 6 (a)–Fig. 6 (c) shows the Souyris recon-structed
results versus the actual radiometric values, and
Fig. 6 (d)–Fig. 6 (f) shows the modified reconstructed re-sults
versus the actual radiometric values.
By comparison, we find that the reconstructed results
of mutual related channels are similar but the Souyris’
method is somewhat inferior. Furthermore, the helix scat-tering
type which is omitted in the Souyris’ reconstruction
by assuming that the reflection symmetry is retained by
the proposed method. The San Francisco test site presents
a better reconstruction performance because the pixels in
this test site are more coherent on average than the Oberp-faffenhofen
test data. Table 1 gives the modes and the stan-dard
deviations of the relative errors associated with the
reconstructed results. The values assessed in the first four
columns are calculated by the method of Souyris’ et al.,
the values assessed in the last four columns are of the pro-posed
method in this paper. Dataset 1 and Dataset 2 denote
the data acquired over the Oberpfaffenhofen area and the
San-Francisco area, respectively. Unit of the phase error is
degree. For example, the relative error for HH polarization
is given by
(|SHH|2CP − |SHH|2FP)/|SHH|2FP. (28)
The mode gives the most frequently occurred value,
which shows the bias from a perfect reconstruction. Let
Dataset 1 denote the Oberpfaffenhofen data, and let
Dataset 2 denote the San Francisco data. All the pixels
of both data sets are used to evaluate the reconstruction
performance. From Table 1, we can see that both methods
overestimate the cross-polarized term, and underestimate
the co-polarized terms. The proposed method resembles
the Souyris’ method in estimating the magnitudes of the
three channels, but is superior for extracting the phase in-formation,
i.e., Angle SHHS∗
VV
.
The estimation of |SHV|2 is the critical point for the
reconstruction algorithms, so we re-assess the estimated
performance of |SHV|2 and SHHS∗
VV
with several typi-cal
regions, i.e., forests, ocean areas, urban regions, farm-lands,
and bare soils. These typical regions are separately
selected from the two data sets, and the selected areas out-lined
by rectangles with indexes have been shown in Fig. 2
and Fig. 4, respectively. The corresponding relative errors
are shown in Table 2. For magnitude reconstruction of the
co-polarized channels, we can see that both the methods
have similar reconstruction accuracies. For magnitude re-construction
of the cross-polarized channel, the proposed
method has a better performance in forests and urban reg-

20. Junjun Yin et al.: Multi-polarization reconstruction from compact polarimetry based on modified four-component scattering... 9
Fig. 6 Distribution of the reconstructed multi-polarization data
Table 1 Modes (Mode) and standard deviations (Std.) of the relative errors associated with the reconstruction algorithms
Souyris’ method Proposed method
Relative Errors
|SHH|2 |SVV|2 |S
HV|2 AngleSHHS∗
VV
HH|2 |S
VV|2 |S
HV|2 AngleSHHS∗
|S
VV
Mode −0.176 9 −0.188 2 0.993 8 0.163 3 −0.160 1 −0.155 0 0.855 0 0.057 6
Dataset 1 Std. 0.090 4 0.115 8 2.011 9 1.814 7 0.093 5 0.116 5 2.014 8 1.053 4
Mode 0.143 4 0.065 2 0.00 8 0.020 0 0.140 2 −0.010 8 0.004 0 0.029 8
Dataset 2 Std. 0.247 4 0.219 0 1.270 6 1.056 3 0.233 0 0.205 4 1.351 2 0.990 6
Table 2 Modes (Mode) and standard deviations (Std.) of the relative errors associated with reconstruction algorithms for some typical areas
Forest Baresoil Farmland Urban area Ocean area
Relative Errors
Mode Std. Mode Std. Mode Std. Mode Std. Mode Std.
|SHH|21 −0.144 2 0.059 7 −0.197 1 0.036 3 −0.194 5 0.039 6 0.206 9 0.210 5 0.095 0 0.088 5
|SVV|21 −0.260 6 0.086 3 −0.244 4 0.052 6 −0.162 5 0.054 0 −0.287 3 0.145 2 0.037 3 0.044 5
|SHV|21 1.061 8 0.414 2 6.535 0 1.327 5 3.840 2 0.958 5 −0.967 0 1.562 1 −0.072 1 1.065 5
Angle SHHS∗
VV
1 0.342 2 2.049 8 0.605 5 3.856 0 0.295 9 0.652 7 −0.041 7 2.120 6 0.233 8 1.633 2
|SHH|22 −0.111 7 0.070 6 −0.175 4 0.031 0 −0.170 8 0.044 5 0.196 5 0.199 6 0.098 2 0.079 7
|SVV|22 −0.230 7 0.116 5 −0.206 7 0.047 8 −0.158 7 0.053 1 −0.141 3 0.034 6 0.036 0 0.044 6
|SHV|22 0.702 1 0.412 0 5.693 8 1.179 4 2.929 9 0.911 3 0.526 2 1.361 0 −0.126 0 0.978 7
Angle SHHS∗
VV
2 0.263 9 1.842 2 0.220 0 1.384 9 0.113 5 0.637 6 0.047 2 1.218 7 0.060 3 1.499 2

21. 10 Journal of Systems Engineering and Electronics Vol. 25, No. 3, June 2014
ions, and the reconstructed biases are smaller. For the
ocean area, the reconstruction of |SHV|2 is not good
because of the low backscattering energy in the cross-polarized
channel from sea surface. For the reconstruc-tion
of SHHS∗
VV
, whose phase information is also the
phase of ρ, the proposed method has a stable superiority
in the phase information extraction. This is because that
the helix scattering component Im(SHHS∗
HV + SHVS∗
VV)
in (13) is used to compensate for the phase information
distortion. Im(SHHS∗
HV + SHVS∗
VV) is generally regarded
as zero under the reflection symmetry assumption and in
fact affects the reconstructed accuracy of the phase of the
co-polarized coherence. The modified method takes this
effect into consideration, revising the imaginary part of
SHHS∗
VV
. Significant improvement can be found with
the selected baresoils and urban areas. But in the area
where the volume scattering is dominant, the improvement
is less because in this circumstance the phase information
is meaningless.
SAR calibration is to provide imagery in which the pixel
values can be directly related to the radar backscatter of the
scene. It is required in accurately estimating of geophysi-cal
parameters. Conventional suggested requirements are
that the radiometric correction is within 0.5 dB and the es-timated
phase error is known to be within 10◦. Thus, we
employ a similar method to quantitatively assess the recon-structions.
The fully polarimetirc SAR data can be seen as
the true backscattered values, and the reconstructed data
from CP are the values needed to be calibrated [14].
Comparisons of both methods have already been shown
in Table 1 and Table 2, which listed the relative errors of
the reconstructed values. Since compact polarimetry needs
higher order statistics [12], the estimated errors are statisti-cally
related to the fully polarimetric data. Take the recon-structed
|SHH|2
π/4 for example. The radiometric bias is
defined as
10 log10(|SHH|2
π/4/|SHH|2FP).
Compared with Dataset 2, Dataset 1 has a relatively
larger error variance, which indicates an expected poor re-construction
performance, so we choose Dataset 1 for as-sessment.
The estimated average reconstructed biases for
|SHH|2 and |SVV|2 are −0.845 5 dB and −0.905 5 dB,
respectively, by Souyris’ method, comparedwith −0.757 7
dB and −0.731 4 dB by the proposed method. Both the re-constructed
magnitude errors of the co-polarized channels
are beyond the suggested limits of ±0.5 dB, but the errors
are all within ±0.8 dB by the proposed method according
to another calibration requirement for some specific ap-plications
[22]. But the reconstruction errors of |SHV|2
by both methods tend to be larger. The reproduced val-ues
are far away from the real radiometric values. This
is because when taking the reconstruction procedure into
consideration, two neglected parts, i.e., Re(SHHS∗
HV) and
Re(SHVS∗
VV), which are ideally regarded as zero by as-suming
the reflection symmetry, are actually added onto
the cross-polarized channel. We take Dataset 1 for exam-ple.
These three parts of the E-SAR test data are compara-ble.
We have
mean
|SHV|2
Re(SHHS∗
HV) + (Re(SHVS∗
VV))
= −4.325 6,
which means that the omitted parts might cause 18% er-ror
at least for this data set theoretically. If the two omitted
parts are comparable with the cross-polarized channel in-tensity,
it is not possible to reproduce |SHV|2 within the
limit of ± 0.5 dB. This is the main reason why the cross-polarized
intensity reconstructed data always tend to be
not accurate. With respect to the phase information recon-struction,
the average phase errors are 2.291◦ and 1.666◦
by the Souyris’ method and the proposed method, respec-tively.
Both of them are within the required error margin of
◦
± 10◦.
4◦
4For typical areas with different scattering mechanisms,
the estimated phase error biases are −12◦, 4.5, 1,
0.49◦, and 1.76◦ by the Souyris’ method, according to
the specific terrain type order listed in Table 2. Labels 1–
5 in Fig. 2 and Fig. 4 present the forests, the baresoils,
farmlands, urban areas, and ocean areas, separately. The
first four rows with subscript 1 are the estimations of the
Souyris’ method, and the last four rows with subscript
2 are the estimations of the proposed method. By the
proposed method, the corresponding estimated phase er-rors
are −9.2◦, 1.65◦, 5.7◦, −0.5◦, and −0.95◦, respec-tively.
The Souyris’ method has a relatively larger phase
error −12◦ in forests and 14◦ in farmlands. In forests,
the double-bounce scattering and the helix scattering are
in general in relatively larger proportion. The proposed
method could compensate for the phase reconstruction dis-tortion
to a certain degree by subtracting the imaginary part
F. For farmlands, where the rough surface scattering often
happens, the backscattered waves might be dominated ei-ther
by odd number or even number reflections [20]. Thus
applying the same extrapolation model (7) to the pixels
with different scattering properties could not yield good
results. For the selected farmland test area, the mean error
of (7) (i.e., the subtraction between the two sides of (7))
is −0.117 5, as compared with −0.007 5 of the improved
model in (19).
The reconstructed values from CP may be not accurate
enough for geophysical parameter estimation. However,

22. Junjun Yin et al.: Multi-polarization reconstruction from compact polarimetry based on modified four-component scattering... 11
it is sufficient for some applications, such as terrain type
classification, metallic target detection, and oil-spill detec-tion.
4.2 Classification performance
To test the classification capability with the reproduced
data from compact polarimetry, classification accuracies of
several typical terrain types with reconstructed data are in-vestigated
in this part. The AIRSAR San Francisco data is
used firstly. The reflection symmetry assumption is valid
in some areas (e.g., the baresoil area and the ocean area),
but not valid in other areas (e.g., the urban area and the for-est
area). The complexWishart maximum likelihood (ML)
classifier is adopted for the supervised classification. Us-ing
the ML classifier, the PolSAR image is classified into
four classes, i.e., ocean surfaces, urban areas, baresoil ar-eas,
and forests.
For valid comparison, the three images (the original FP
image, the reconstructed image by the Souyris’ method,
the reconstructed image by the proposed method) are clas-sified
using the same training samples. To quantitatively
compare the classification accuracy, we regard the clas-sified
results using the original FP data as the reference
map. Though the classification results of the FP data are
not completely consistent with the real ground truth mea-surements,
they are reasonable for classification evaluation
of compact polarimetry. The supervised classification ac-curacy
of the ML classifier is somewhat related to the se-lected
training samples, but an average experimental re-sult
could reduce this influence. No matter what kind of
the classifier is applied, it does not affect the assessment
of the multi-polarization reconstruction algorithm as long
as the classifier is valid. The confusion matrices relating
to both the reconstruction algorithms are listed in Table 3,
expressed in percentage. The classification rates are aver-age
of several experiments, and the sum of each column
is 1. We can observe that the classification accuracy with
the data reproduced by the proposed algorithm is better,
especially for the forest classification.
Table 3 Terrain type classification accuracies (presented in percent-age)
of San Francisco data set
(a) Data reproduced by the proposed method.
FP
CP
Ocean area Urban area Baresoil Forest
Ocean 0.981 0 0.092 0.000
Urban 0 0.896 0.001 0.011
Bare-soil 0.019 0 0.648 0.033
Forest 0 0.104 0.259 0.956
(b) Data reproduced by the Souyris’ method
FP
CP
Ocean area Urban area Baresoil Forest
Ocean 0.972 0 0.074 0.006
Urban 0 0.871 0.000 0.070
Baresoil 0.027 0.020 0.611 0.030
Forest 0 0.108 0.314 0.892
The classified result for forests with the reproduced data
by the proposed method is close to the classified result with
the original fully polarimetric data, but the result by the
Souyris’ method is not good enough. The standard devia-tion
of the relative error, which is defined in (28), is a good
measure for precision. For forests, the relative mean square
errors of |SHV|2 estimated by the Souyris and proposed
methods are 1.817 and 0.432, respectively. Next, the total
classification accuracy is considered,which is an important
parameter and could show the quality of the reconstructed
data. From Table 3, it is observed that the data reproduced
by the proposed method give a total classification accuracy
of 87.03%, which is the average of the diagonal values in
Table 3 (a). It is higher than the average rate 83.71% relat-ing
to the Souyris’ method shown in Table 3 (b).
The second data set used for assessment is the Oberp-faffenhofen
data. The target classes over this area are com-plicated.
Using the ML classifier, we simply classify this
image into four classes, i.e., forests, buildings, the flat-ground,
and farmlands. The confusion matrices are shown
in Table 4. The classification results of the original fully
PolSAR data are also used as the reference for evalua-tion.
From inspection of Table 3 and Table 4, the classifi-cation
capability of the reconstructed data by the proposed
method is acceptable, which shows the effectiveness of the
developed method for the application of terrain classifica-tion.
Table 4 Terrain type classification accuracies (expressed in percent)
of Oberpfaffenhofen area
(a) Classification with the data reproduced by the proposed method.
FP
CP
Forest Flat-ground Building Farmland
Forest 0.892 0 0.335 0
Flat-ground 0 0.939 0 0
Building 0.037 0 0.665 0
Farmland 0.071 0.061 0 1
(b) Classification with the data reproduced by the Souyris’ method
FP
CP
Forest Flat-ground Building Farmland
Forest 0.876 0 0.329 0.004
Flat-ground 0.004 0.936 0 0.003
Building 0.048 0 0.671 0
Farmland 0.072 0.064 0.0000 0.993
5. Conclusions
Based on amodified four-component model-based decom-

23. 12 Journal of Systems Engineering and Electronics Vol. 25, No. 3, June 2014
position, an improvedmulti-polarization reconstruction al-gorithm
has been proposed in this paper for the π/4 com-pact
polarimetry. In the proposed reconstruction algorithm,
we consider the non-reflection symmetric scattering case,
and recover more information. A special volume scatter-ing
model, which is more consistent with the assumption
of fully depolarized backscattering scenario, is employed
to decompose the target scattering coherency matrix. In
this way, a simple relationship between the helix scattering
and the volume scattering components is derived. Then the
relationship is used to compensate for the phase informa-tion
distortion when implementing the reconstruction. Us-ing
the decomposed powers of the four scattering com-ponents
and considering the respective polarimetric prop-erties,
we establish an average polarization state model
and then present the reconstruction procedure. The pro-posed
algorithm takes account of the non-reflection sym-metry
condition and the physical scattering mechanisms,
and thus has a better reconstruction performance compared
with the Souyris’ method, which is demonstrated by its
implementations on two PolSAR data sets. Experimental
results show that the proposed method is more suitable for
terrain type analysis.
References
[1] J. S. Lee, M. R. Grunes, T. L. Ainsworith, et al. Unsupervised
classification using polarimetric decomposition and the com-plex
Wishart classifier. IEEE Trans. on Geoscience and Re-mote
Sensing, 1999, 37(5): 2249–2258.
[2] K. Ersahin, I. G. Cumming, R. K. Ward. Segmentation and
classification of polarimetric SAR data using spectral graph
partitioning. IEEE Trans. on Geoscience and Remote Sensing,
2010, 48(1): 164–174.
[3] C. He, G. Xia, H. Sun. SAR images classification method
based on dempster-shafer theory and kernel estimate. Journal
of Systems Engineering and Electronics, 2007, 18(2): 210–
216.
[4] D. Lu, Q.Weng. A survey of image classification methods and
techniques for improving classification performance. Interna-tional
Journal of Remote Sensing, 2007, 28(5): 823–870.
[5] D. H. Hoekman, M. J. Quiriones. Land cover type and biomass
classification using AirSAR data for evaluation of monitoring
scenarios in the Colombian Amazon. IEEE Trans. on Geo-science
and Remote Sensing, 2000, 38(2): 685–696.
[6] D. L. Schuler, J. S. Lee. Mapping ocean surface features us-ing
biogenic slick fields and SAR polarimetric decomposition
techniques. Electronic Engineering-Radar, Sonar, Navigation,
2006, 153(3): 260–270.
[7] F. F. Gama, J. Santos, J. Mura. Eucalyptus biomass and vol-ume
estimation using interferometric and polarimetric SAR
data. Remote Sensing, 2009, 12(3): 939–956.
[8] J. C. Souyris, C. Henry, F. Adragna. On the use of complex
SAR image spectral analysis for target detection: assessment
of polarimetry. IEEE Trans. on Geoscience and Remote Sen-sing,
2003, 41(12): 2725–2734.
[9] J. Li, P. Huang, X. Wang, et al. Image edge detection based on
beamlet transform. Journal of Systems Engineering and Elec-tronics,
2009, 20(1): 1–5.
[10] Y. Cui, J. Yang, X. Zhang. New CFAR target detector for SAR
images based on kernel density estimation and mean square er-ror
distance. Journal of Systems Engineering and Electronics,
2012, 23(1): 40–46.
[11] J. S. Lee, M. R. Grunes, E. Pottier. Quantitative comparison
of classification capability: fully polarimetric versus dual and
single-polarization SAR. IEEE Trans. on Geoscience and Re-mote
Sensing, 2001, 39(11): 2343–2351.
[12] J. C. Souyris, P. Imbo, R. Fjørtoft, et al. Compact polarimetry
based on symmetry properties of geophysical media: the π/4
mode. IEEE Trans. on Geoscience and Remote Sensing, 2005,
43(3): 634–646.
[13] J. C. Souyris, N. Stacy, T. Ainsworth, et al. SAR compact po-larimetry
for earth observation and planetology: concept and
challenges, a study case at P band. Proc. of the Polarimetric
and Interferometric SAR Workshop, 2007.
[14] M. E. Nord, T. L. Ainsworth, J. S. Lee, et al. Comparison
of compact polarimetric synthetic aperture radar modes. IEEE
Trans. on Geoscience and Remote Sensing, 2009, 47(1): 174–
188.
[15] T. L. Anisworth, M. Preiss, N. Stacy, et al. Analysis of com-pact
polarimetric SAR imaging modes. Proc. of the Polarimet-ric
and Interferometric SAR Workshop, 2007.
[16] Y. Yamaguchi, T.Moriyama, M. Ishido, et al. Four-component
scattering model for polarimetric SAR image decomposi-tion.
IEEE Trans. on Geoscience and Remote Sensing, 2005,
43(8): 1699–1706.
[17] Y. Yajima, Y. Yamaguchi, R. Sato, et al. POLSAR image anal-ysis
of wetlands using a modified four-component scattering
power decomposition. IEEE Trans. on Geoscience and Remote
Sensing, 2008, 46(6): 1667–1673.
[18] A. Freeman. Fitting a two-component scattering model to po-larimetric
SAR data from forests. IEEE Trans. on Geoscience
and Remote Sensing, 2007, 45(8): 2583–2592.
[19] A. Freeman, S. L. Durden. A three-component scattering
model for polarimetric SAR data. IEEE Trans. on Geoscience
and Remote Sensing, 1998, 36(3): 963–973.
[20] J. van Zyl. Unsupervised classification of scattering behavior
using radar polarimetry data. IEEE Trans. on Geoscience and
Remote Sensing, 1989, 27(1): 36–45.
[21] S. V. Nghiem, S. H. Yueh, R. Kwok, et al. Symmetry properties
in polarimetric remote sensing. Radio Science, 1992, 27(5):
693–711.
[22] P. Dubois, D. Evans, J. van Zyl. Approach to derivation of
SIR-C science requirements for calibration. IEEE Trans. on
Geoscience and Remote Sensing, 1992, 30(6): 1145–1149.
Biographies
Junjun Yin was born in 1983. Now she is a
Ph.D. candidate in the Department of Electronic
Engineering, Tsinghua University, Beijing. Her re-search
interests include compact polarimetry, ship
and oil-spill detections in multi-polarization SAR
imagery, and terrain type clas sification and segmen-tation.
E-mail:yinjj07@gmail.com
Jian Yang was born in 1965. He received his
B.S. and M.S. degrees from Northwestern Polytech-nical
University, Xi’an, China, in 1985 and 1990,
respectively, and Ph.D. degree from Niigata Univer-sity,
Niigata, Japan, in 1999. In 1985, he joined the
Department of Applied Mathematics, Northwest-ern
Polytechnical University. From 1999 to 2000,
he was an assistant professor with Niigata Univer-sity.
In April 2000, he joined the Department of Electronic Engineering,
Tsinghua University, Beijing, China, where he is now a professor. His re-search
interests include radar polarimetry, remote sensing, mathematical
modeling, optimization in engineering, and fuzzy theory.
E-mail: yangjian.ee@gmail.com