TU1.L09.1 - APPLICATION OF POLARIMETRIC SAR TO EARTH REMOTE SENSING

National Aeronautics and Space Administration

Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California

Application of Polarimetric SAR to Earth Remote Sensing

Jakob van Zyl and Yunjin Kim

Jet Propulsion LaboratoryCalifornia Institute of Technology


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Overview

• Polarimetric SAR data are becoming more available, both in single pass and interferometric form

• Because the full vector nature of the electromagnetic wave is preserved, theoretically one could perform a more complete analysis of scattering

• There are many different ways to approach the analysis of a polarimetric data set.– New users are often overwhelmed and confused– It is vitally important that the polarimetric community

provides simple guides on how to analyze data.


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Basic Tools: Polarization Signature

• The polarization Signature is a simple graphical way to display the radar cross-section as a function of polarization.

• Usually display co- and cross-polarization signatures



Polarization Signatures A New Perspective


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Dihedral Corner Reflector


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Rotated Dihedral


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Three Orthogonal Scatterers

These are also the eigenvectors of the Pauli basis

Trihedral Dihedral Rotated Dihedral


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Effect of Phase Calibration Error

No Error 45 Degrees

90 Degrees

135 Degrees180 DegreesThe signature is rotated about the S1 axis by half the phase calibration error value. Co-pol nulls are in the S2-S3 plane.


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Effect Of Co-Channel Imbalance

Signatures are distorted. Co-pol nulls are in the S1-S3 plane


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Dipole Orientation

Horizontal 45 Degrees Vertical

The angle of the co-pol maximum relative to the S1 axis is exactly twice the orientation angle of the dipole


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California What do we Have Here?


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Polarization Synthesis


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Check Signatures


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Signature Analysis

• Comparing polarization signatures in an image with those from simple scatterers is a simple way to infer what scattering mechanisms were present in an image

• Checking signatures on a pixel by pixel basis is very tedious and unrealistic as an analysis tool

• Our analysis techniques must be amenable to image processing


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Eigenvector Decomposition (Cloude)

• Cloude showed that a general covariance matrix can be decomposed as follows:

• Here, are the eigenvalues of the covariance matrix, are its eigenvectors, and means the adjoint (complex conjugate transposed) of .

• In the monostatic (backscatter) case, the covariance matrix has one zero eigenvalue, and the decomposition results in at most three nonzero covariance matrices.

T

T 1k1 k1† 2k2 k2

† 3k3 k3† 4k4 k4

†

i , i 1,2,3,4

k i , i1,2,3,4 k i†

k i



• The eigenvectors for terrain with reflection symmetry are

2

1 2 2

2

2 2 2

3

2

04 1

2

04 1

0

1

0

e

e

e



• Note that

*

* * *1 2 2 1

21 2 1

0 1 ; phase phasehh vv hh hhhh vv hh vv

vvvv hh vv

e e e ee e e e

ee e e

e e

hh vve e

hh vve e

1

-1

-1

1

1,2e

2,1e


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Eigenvalue Images


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Pauli Scattering Decomposition


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Single vs Double Reflections

0.0

0.2

0.4

0.6

0.8

1.0

10 20 30 40 50 60 70 80

Angle of Incidence

Rel

ativ

e R

atio

hh vvS S

Double Reflection / Single Reflection

Dielectric Constant = 81


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Measures of Scattering Randomness

• Entropy (Cloude, Pottier..)

• Radar Vegetation Index (van Zyl and Kim)

• Pedestal Height (van Zyl, Durden et al.)

3

31 1 2 3

log ; iT i i i

i

H P P P

1 2 3

1 2 3

4min , , 8

2hv

hh vv hv

RVI

1 2 3

1 2 3

min( , , )

max( , , )Pedestal Height


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Scatterer Randomness

These images convey the same information. The details differ only because ofscaling and linearity.



Scattering Mechanisms van Zyl 1989


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Alpha/Entropy Classification

• Cloude and Pottier (1996) proposed the following description for the eigenvectors of the covariance matrix:

• The average alpha angle is then calculated using

cos sin cos sin sini ie e e

3

1i i

i

P


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Alpha/Entropy Classification


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Black Forest, Germany


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Eigenvector Decomposition


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Model Based Decomposition

• Model based algorithms decompose an observed covariance matrix in terms of known (and expected) model derived covariance matrices.

• All individual covariance matrices must satisfy some basic requirements– The observed scattering power for any polarization

combination can never be negative– We can use this fact to determine the allowable values of a in

the decomposition above

model remaindera C C C


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Model Based Decomposition

• The eigenvalues of the following matrix must be zero or positive:

• The maximum value of a that can be used is that value that ensures non-negative eigenvalues for the matrix on the right.

remainder modela C C C


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Example: Freeman and Durden


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Example: Yamaguchi et al.


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Non-Negative Eigenvalue Decomposition

• The non-negative eigenvalue decomposition starts with a model for the canopy scattering and subtracts that from the observed covariance matrix

• The remainder matrix is then further decomposed using an eigenvector decomposition– The first two eigenvectors are interpreted as odd and even

numbers of reflections (single and double reflections)

c canopy d double s single r remainderf C C C C C

van Zyl, Arii and Kim, “Model-Based Decomposition of Polarimetric SAR Covariance, Matrices Constrained for Non-Negative Eigenvalues” In Press, IEEE Trans. On Geosci and Remote Sens., 2010


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Comparison with Freeman and Durden


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Adaptive Model-Based Decomposition

• The non-negative eigenvalue decomposition provides a simple way to compare different models to find which is the best fit to the observation– Different models are compared by observing the total

power left in the remainder matrix– The model that leaves the least power in the

remainder matrix provides the best fit

c canopy d double s single r remainderf C C C C C


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Example


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Arii et al. Adaptive Decomposition

• Arii et al. (2010) proposes a decomposition algorithm to analyze polarimetric images– The canopy scattering is described by a generalized canopy scattering model – The canopy is described in terms of a randomness parameter and a mean

orientation angle

Arii, van Zyl and Kim, “Adaptive Model-Based Decomposition of Polarimetric SAR Covariance Matrices,” In Press, IEEE Trans. On Geosci and Remote Sens., 2010

20cos npdf

0 0 0

12, 2 4

1 1 2vol

n nnC n C C C

n n n

2cos 2 2 sin 2 0 cos 4 2 sin 4 cos 43 0 1

1 1 10 2 0 ; 2 2 sin 2 0 2 sin 2 ; 4 2 sin 4 2cos4 2 sin 4

8 8 81 0 3 0 2 sin 2 2cos2 cos4 2 sin 4 cos 4

C C C


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Generalized Canopy Model

Arii, van Zyl and Kim, “A General Characterization for Polarimetric Scattering from Vegetation Canopies,” In Press, IEEE Trans. On Geosci and Remote Sens., 2010

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.01 0.1 1 10 100

Entr

opy

Power of Cosine Squared



Adaptive Decomposition Results Mean Orientation Angle

P-bandC-band L-band

Vertical Horizontal


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Azimuth Slopes



Adaptive Decomposition ResultsRandomness

delta

P-bandC-band L-band

uniformcos_sq


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Model-Based Decompositions

• Model-based decompositions allow the analyst to inject human knowledge into the investigation

• For this type of investigation to make sense, the models should be applicable to the image being analyzed

• One may have to take terrain effects into account when performing the decomposition by first removing the effects of azimuth rotations


Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California Summary

• Polarimetric radar images provide the opportunity to learn about the scattering mechanisms that dominate in each pixel.

• Simple tools can provide a quick overview of the scattering present in an image.

• Model-based decomposition is a simple way to identify the most appropriate model that best describes the observed scattering in each pixel

• Once the most appropriate models are identified, further quantitative analysis can be performed.

TU1.L09.1 - APPLICATION OF POLARIMETRIC SAR TO EARTH REMOTE SENSING

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