Yamaguchi 4 components decomposition
Description
There is currently a great deal of interest in the use of
polarimetry for radar remote sensing. In this context, an important objective
is to extract physical information from the observed scattering of microwaves
by surface and volume structures. The most important observable measured by
such radar systems is the 3x3 coherency matrix [T3]. This matrix accounts for local variations in the scattering
matrix and is the lowest order operator suitable to extract polarimetric
parameters for distributed scatterers in the presence of additive (system)
and/or multiplicative (speckle) noise.
Many targets of interest in radar remote sensing require a
multivariate statistical description due to the combination of coherent speckle
noise and random vector scattering effects from surface and volume. For such
targets, it is of interest to generate the concept of an average or dominant
scattering mechanism for the purposes of classification or inversion of
scattering data. This averaging process leads to the concept of the « distributed target » which has its
own structure, in opposition to the stationary target or « pure single target ».
Target Decomposition theorems are aimed at providing such an
interpretation based on sensible physical constraints such as the average
target being invariant to changes in wave polarization basis.
Target Decomposition theorems were first formalized by J.R. Huynen
but have their roots in the work of Chandrasekhar on light scattering by small
anisotropic particles. Since this original work, there have been many other
proposed decompositions. We classify four main types of theorem:
1. Those employing coherent decomposition of the
scattering matrix (Krogager, Cameron).
2. Those based on the dichotomy of the Kennaugh
matrix (Huynen, Barnes).
3. Those based on a “model-based” decomposition of
the covariance or the coherency matrix (Freeman and Durden, Dong).
4. Those using an eigenvector / eigenvalues
analysis of the covariance or coherency matrix (Cloude, VanZyl, Cloude and
Pottier).
The Yamaguchi 4 components decomposition is directly based on the Freeman-Durden 3 components decomposition
which models the scattering power in three distinct components
and which can be successfully applied to decompose SAR observations under the
reflection symmetry condition. However, it can be possible to find some areas
in a SAR image for which the reflection symmetry condition does not hold.
Based on the Freeman-Durden 3 components decomposition, Yamaguchi et al.
proposed, in 2005, a 4-component scattering model by introducing an additional
term corresponding to non-reflection symmetric cases 
and 
.
In order to accommodate the decomposition scheme for the
more general scattering case encountered in complicated geometric scattering
structures, the fourth component introduced is equivalent to a helix scattering
power. This helix scattering power term, that corresponds to and , appears
in heterogeneous areas (complicated shape targets or man-made structures)
whereas disappears for almost all natural distributed scattering.
The concept of helix mechanism has
been mainly developed by Krogager in his coherent Target Decomposition Theorem,
where it was shown that a helix target generates a left-handed or a
right-handed circular polarization for all incident linear polarizations,
according to the target helicity. The scattering matrices, corresponding to a
left-helix target or to a right-helix target, have the form: 
and 
.
These two scattering matrices yield
left / right helix covariance matrices given by.
and 
where in both case, fC
corresponds to the contribution of the helix scattering component.
The second important contribution
concerns the modification of the volume scattering matrix in the decomposition
according to the relative backscattering magnitudes of 
versus 
. In the
theoretical modeling of volume scattering, a cloud of randomly oriented dipoles
is implemented with a probability function being uniform for the orientation
angles. However, for vegetated areas where vertical structure seems to be
rather dominant, the scattering from tree trunks and branches displays a
non-uniform angle distribution. The proposed new probability distribution is
given by 
where θ is taken from the horizontal axis seen from the
radar.
It follow
that in the case of:
●
a cloud of
randomly oriented, very thin horizontal (
)
cylinder-like scatterers, the volume scattering averaged covariance matrix 
is thus given by 
●
a cloud of
randomly oriented, very thin vertical (
)
cylinder-like scatterers, the volume scattering averaged covariance matrix is thus given by
In both case,
fV corresponds to the contribution of the
volume scattering component.
The asymmetric form of the two volume scattering
averaged covariance matrices seems to be of considerable use because it can
be adjusted to the measured data according to the ratio 
.
Depending on the scene, the Yamaguchi 4 components decomposition
proposes to select the appropriate volume scattering averaged covariance
matrices by choosing one of the asymmetric forms if the
relative magnitude difference is larger than 2dB, or the symmetric
form if the difference is within ±2dB.
As a result, this choice allows
making a straightforward best fit to measured data.
Assuming that the volume,
double-bounce, surface and helix scatter components are uncorrelated, the total
second-order statistics are the sum of the above statistics for the individual
mechanisms. Thus, the model for the total backscatter is:
This model gives five equations in six unknowns 
. The parameters a,
b, c and d are fixed according to the chosen
volume scattering averaged covariance matrix .
The contribution of each scattering mechanism can be estimated to
the span, following 
with:
The term fv
corresponds to the contribution of the volume scattering of the final
covariance matrix 
. The power
scattered by the double-bounce component of the final covariance matrix has the expression 
and the power scattered by the surface-like
component is 
. At last,
the term fC corresponds to
the contribution of the helix scattering of the final covariance matrix .
Although the Yamaguchi 4
components decomposition is intended to apply to non-reflection symmetry
case, the scheme automatically includes the reflection symmetry condition, thus
proposing a decomposition scheme for the more general scattering case
encountered in complicated geometric scattering structures.
There exist
three mode of decomposition which are the following.
o
Y4O:
original Yamaguchi 4 components decomposition
o
Y4R:
Yamaguchi 4 components decomposition with rotation transformation
o
S4R:
original Yamaguchi 4 components decomposition with special unitary
transformation from oriented dihedral component.
The following figures present the scheme employed to invert the Yamaguchi 4 components decomposition according
to the decomposition used.
Y4O
decomposition mode
Y4R
decomposition mode
S4R
decomposition mode
References
Books:
● Jong-Sen
LEE – Eric POTTIER, Polarimetric Radar Imaging: From basics to
applications, CRC Press; 1st
ed., February 2009, pp 422, ISBN: 978-1420054972
● Shane
R. CLOUDE, Polarisation: Applications in
Remote Sensing, Oxford
University Press, October 2009, pp 352, ISBN: 978-0199569731
● Charles
ELACHI – Jakob J. VAN ZYL, Introduction To The Physics and Techniques of Remote Sensing, Wiley-Interscience;
2nd edition (July 31, 2007), ISBN-10 0-471-47569-6, ISBN-13 978-0471475699
● Harold
MOTT, Remote Sensing with Polarimetric
Radar, Wiley-IEEE Press; 1st
edition (January 2, 2007), ISBN-10 0-470-07476-0, ISBN-13 978-0470074763
● Jakob
J. VAN ZYL – Yunjin KIM, Synthetic Aperture Radar Polarimetry, Wiley; 1st edition (October 14, 2011), ISBN-10
1-118-11511-2, ISBN-13 978-1118115114
● Yoshio
Yamaguchi, Polarimetric SAR Imaging : Theory and
Applications, CRC Press; 1st ed., August 2020, pp 350, ISBN: 978-1003049753
● Irena
HAJNSEK – Yves-Louis DESNOS (editors), Polarimetric
Synthetic Aperture Radar : Principles and
applications, Springer; 1st edition (Marsh 30, 2021), ISBN
978-3-030-56502-2
Journals:
●
Freeman A. and Durden S., “A three-component scattering model to
describe polarimetric SAR data,” in Proc. SPIE Conf. Radar Polarimetry, vol.
SPIE-1748, pp. 213-225, San Diego, CA, July 1992.
●
Freeman A. and Durden S., “A Three-Component Scattering Model for
Polarimetric SAR Data”, IEEE Trans. Geosci. Remote
Sens., vol. 36, no. 3, May 1998.
●
Krogager E. and Freeman A., “Three component break-downs
of scattering matrices for radar target identification and classification”, in
Proc. PIERS '94, Noordwijk, The Netherlands, July
1994.
●
Yamaguchi Y., Moriyama T., Ishido M. and Yamada
H., “Four-Component Scattering Model for Polarimetric SAR Image
Decomposition”, IEEE Trans. Geos. Remote Sens., vol. 43, no. 8, August
2005.
●
Yamaguchi Y., Yajima Y. and Yamada H., “A
Four-Component Decomposition of POLSAR Images Based on the Coherency Matrix”,
IEEE Geos. Rem. Sens. Letters, vol. 3, no. 3, July 2006.
●
Y. Yamaguchi, A. Sato, W.M. Boerner, R. Sato, H.
Yamada, “4-component scattering power decomposition with rotation of coherency
matrix”, IEEE TGRS vol. 49, no. 6, June 2011
●
A. Sato, Y. Yamaguchi, G. Singh, and S.-E. Park, “4-component
scattering power decomposition with extended volume scattering model”, IEEE
GRS Letters, vol. 9, no. 2, pp. 166–170, March 2012
●
G. Singh, Y. Yamaguchi, S.E. Park, Y. Cui, H. Kobayashi, « Hybrid Freeman/Eigenvalue Decomposition
Method With Extended Volume Scattering Model » IEEE
GRS Letters, vol. 10, no. 1, January 2013
●
G. Singh, Y. Yamaguchi, S.E. Park, « General Four-Component
Scattering Power Decomposition With Unitary
Transformation of Coherency Matrix » IEEE TGRS vol. 51, no. 5, May 2013