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PolSAR-Ap: Basic Principles of SAR PolarimetryCarlos López-Martínez
Remote Sensing LaboratorySignal Theory and Communucations Dept.Universitat Politècnica de Catalunya UPC
Barcelona, SPAIN
Motivation
•SAR Polarimetry is characterized by Mathematical and Signal Processing backgroundsthat need to be correctly introduced for a better understanding of the applicationsand the extraction of quantitative biophysical and geophysical parameters
•Reviewed and complemented theoretical background with new topics and newreferences (publications, books) according to the different applications selected toillustrate the PolSAR Application Demonstration
•Establishment of a common mathematical formulism
•To provide a self-contained manuscript
•Limited theoretical view. Introduction on basic concepts and ideas necessary for acomplete analysis and development of the different applications selected to illustratethe PolSAR Application Demonstration
Basic Aspects Presented
• Theory of Radar Polarimetry– Wave polarimetry
– Scattering polarimetry
• SAR Data Statistical Description and Speckle Noise Filtering– Statistical characterization of PolSAR data
– Definition of the polarimetric coherence and the Covariance and Coherency matrices
– Polarimetric Speckle Noise Filtering
• Polarimetric Scattering Decomposition Theorems
• Polarimetric SAR Interferometry
• Polarimetric SAR Tomography
• References
Theory of Radar Polarimetry
• Definition: Polarimetry refers specifically to the vector nature of theelectromagnetic waves, whereas radar polarimetry is the science of acquiring,processing and analyzing the polarization state of an electromagnetic wave inradar applications:
– Wave polarimetry that deals with the representation and the understandingof the polarization state of an electromagnetic wave
– Scattering polarimetry collects the topic of inferring the properties of a giventarget, from a polarimetric point of view, given the incident and the scatteredpolarized electromagnetic waves
Theory of Radar Polarimetry
• Starting Point: Space-Time evolution of the real electromagnetic fieldElectromagnetic field
x
y
Polarization Ellipse for z0
0
0
cos
, cos
0
x x x
y y y
z
E E t kz
E z t E E t kz
E
Theory of Radar Polarimetry
• Starting Point: Space-Time evolution of the real electromagnetic fieldElectromagnetic field
0
0
cos
, cos
0
x x x
y y y
z
E E t kz
E z t E E t kz
E
Theory of Radar Polarimetry
• Description of the polarization ellipse
– Totally polarized waves• Geometrical description
• Jones vector
• Stokes vector
• Description of the canonical polarization states (linear, circular, …)
– Partially polarized waves• Coherency matrix/vector
• Stokes vector
• Change of polarization basis and Polarization Synthesis
1
ˆ ˆ,
xu
yu
EE
EE
u u
U
Theory of Radar Polarimetry
• Scattering polarimetry: Introduction of the concept of scattering matrix
• Introduction of conventions
– Forward scattering
– Backscattering
– FSA Alignment convention
– BSA Alignment convention
• Canonical scattering mechanisms
s ijkrhh hvh h
s ivh vvv v
S SE Ee
S SrE E
Sphere
1 0
0 12
a
S
Trihedral Corner Reflector
2 1 0
0 112
kl
S
Theory of Radar Polarimetry
• Key concept: Scattering vector, i.e., vectorization of the scattering matrix
• Key concept: Hermitian product of target vector (backscattering direction under the BSA convention)
1
2
hh vvhh
hh vvhv
l p
hv vhvh
hv vhvv
S SS
S SS
S SS
j S SS
k k1
22
2
hh hh vv
l hv p hh vv
vv hv
S S S
S S S
S S
k k
2 * *
2* * *
2* *
2
2 2
2
hh hh hv hh vv
T
l l hv hh hv hv vv
vv hh vv hv vv
S S S S S
S S S S S
S S S S S
k k
*2 *
* 2* *
* * 2
2
2
2 2 4
hh vv hh vv hh vv hh vv hv
T
p p hh vv hh vv hh vv hh vv hv
hv hh vv hv hh vv hv
S S S S S S S S S
S S S S S S S S S
S S S S S S S
k k
Theory of Radar Polarimetry
• Single, Dual, Compact and Full Polarimetry
Courtesy of Dr. R. K. Raney
SAR Data Statistical Description
• Starting point: Speckle noise scattering model or Random Walk. Constructive and destructive interference that appears in coherent imaging systems
• SAR data must be considered statistically to account fot the speckle noise effect
– One-dimensional Gaussian distribution (Single SAR image)
– Multidimensional Gaussian distriibution (Target vectors)
Radarsat-2 amplitude image o the scattering matrix element over San Francisco (USA)hhS
SAR Data Statistical Description
• Key concept: The Covariance and the Coherency matrices (backscattering directionunder the BSA convention)
• Key concept: The polarimetric coherence
2 * *
2* * *
2* *
2
2 2
2
hh hh hv hh vv
T
l l hv hh hv hv vv
vv hh vv hv vv
E S E S S E S S
E E S S E S E S S
E S S E S S E S
C k k
*2 *
* 2* *
* * 2
2
2
2 2 4
hh vv hh vv hh vv hh vv hv
T
p p hh vv hh vv hh vv hh vv hv
hv hh vv hv hh vv hv
E S S E S S S S E S S S
E E S S S S E S S E S S S
E S S S E S S S E S
T k k
2 2
xk lj
k l
E S Se
E S E S
SAR Data Statistical Description
• Speckle noise filtering: Estimation of the Covariance and Coherency matrices
Radarsat-2 polarimetric RGB image over San Francisco(USA) where the colour code is: Shh blue, Svv red andShv green. (a) Original image and (b) Filtered imagewith a 7x7 multilook filter
|Svv| |Shv| |Shh|
Polarimetric Target Decomposition Theorems
• Decomposition of the Scattering or the Coherency and Covariance matrices for a better interpretation
– Coherent Target Decomposition Theorems
• Pauli decomposition
– Incoherent Target Decomposition Theorems
• Three-component Freeman Decomposition
• Four-Component Yamaguchi Decomposition
• Non-Negative Eigenvalue Decomposition
• Eigenvector-Eigenvalue based Decomposition (Entropy, Anisotropy and Mean Alpha Angle)
1
k
i i
i
c
S S
1
k
i i
i
p
C C1
k
i i
i
q
T T
Polarimetric Target Decomposition Theorems
10
H
A
10
900
Radarsat-2 polarimetric RGB image over San Francisco (USA)
Polarimetric SAR Interferometry
• Study variation of the interferometric coherence with polarization to studyvolumetric scatterers
– Single Channel Interferometry
– Multi Channel Interferometry
• Optimization of interfeometric coherence (Max and Mins)
• Model based PolInSAR: Random Volume over Ground Model (RVoG)
*
1 2
* *
1 1 2 2
iE S S
eE S S E S S
1 12 21 2
1 11 1 2 22 2
,.
H
H H
w Ω ww w
w T w w T w
11 12
1 2
12 22
H
T ΩΛ T Λ
Ω T
Polarimetric SAR Tomography
• Key concept: 3-D SAR Tomography (SARTom) is an experimental multibaseline (MB)interferometric mode achieving full 3-D imaging in the range-azimuth-height spacethrough elevation beam forming, i.e. spatial (baseline) spectral estimation
– SARTom can add more features for the analysis of complex scenarios, e.g. for theestimation of forest height and biomass, sub-canopy topography, soil humidity and icethickness monitoring, and extraction of heights and reflectivities in layover urban areas
– Polarimetric SAR Tomgraphy (PolSARtom) jointly exploits MB SAR data acquired withdifferent polarization channels to improve the accuracy of the estimation of the verticalposition of the imaged scatterers, and to estimate a set of normalized complexcoefficients characterizing the corresponding polarimetric scattering mechanism
• Aspects descrived:– SARtom and PolSARTom as Spectral Estimation Problems: Non-model Based Adaptive
Solutions
– Model-based PolTomSAR
– Coherence Tomography
Conclusions• Limited theoretical view. Introduction on basic concepts and ideas necessary for a
complete analysis and development of the different applications selected toillustrate the PolSAR Application Demonstration
• Complete theoretical view as references/bibliography. Main references:
• Complementarity with other books
