two-point statistic of polarimetric sar data two-point statistic of polarimetric sar data
TRANSCRIPT
G. F. De Grandi1, R.M. Lucas2, A. Bouvet1
European Commission Joint Research Centre21027, Ispra (VA), Italy
e-mail: [email protected]
Two-point statistic of polarimetric SAR data provided by a wavelet frame
The importance of being scaling…(suggested by Oscar Wilde)
Institute of Geography and Earth SciencesAberystwyth University, Aberystwyth, UK,
SY23 3DB.e-mail: [email protected]
Bits of History
Problem Statement
vvhvhh SSS 2
Two-point statistic provided by wavelet
coefficients
Structure Function
2)()()( xfxff
Wavelet Variance
)()(2 scalefxw
Spatial random field (SRF)
Tvvhvhh SSS 2
),(),( * yxSSyxP hvhvhv
Wavelet frame transform
What happens when the polarization basis is changed?
vvhvhh SSS 2
Wavelet variance of the crospolar and
copolar power in the rotated polarization
basis
),()(2 fxw
Tvvhvhh SSS 2
),,(),,( '*2
'2 yxyxPxpol
T' 2cos1
2sin
),,(),,( '*1
'1 yxyxPcopol
Wavelet variance of PolSAR power in a rotated basis: a model for a WS stationary process
vvhvhh SSS 2
Hj Fourier transform of the wavelet dilated at scale j
jH
ACF of wavelet coefficients computed in the frequency domain from the
power spectrum G of the input process 21 jinout HGR
outG inG
0Rw out2i Wavelet variance at cross-polarized
state with orientation ψ
Wavelet transformPower
spectrum inPower
spectrum out
Power spectrum of the crosspolar power in the rotated basis
vvhvhh SSS 2 VVHVHH S,S2,S
HHVVHVSScScS
21
Rotation to a linear basis with orientation ψ
Cross-polarized component in the new basis ψ
ii
iab XaP )(
**2 Re)( jijij
iiii
iab SSccSScP
VVHVHHi SSSS ,,
2cos21c
2sin2
22c
Power spectrum of the input process
j
jji
iiin XaXaG *)(
jii XXj
ijiX
iiin
GaaGaG,
2)(
**2 Re)( jijij
iiii
iab SSccSScP
ii
iab XaP )(
Power spectrum in the rotated basis is a linear combination of the power spectra (auto-correlation) and cross-spectra (cross correlation) between dyads of the vector in the H,V basis
Copol-xpol correlation
Power-Correlation
HV2
HH2, VV2
A numerical model for the wavelet variance of a correlated K-distributed stationary clutter
vvhvhh SSS 2
The Wavelet Scaling Polarimetric Signature (WASPS)
),()(2 fxw
Correlated K-distributed clutter, C. Oliver
From theory to practice
vvhvhh SSS 2
Multi-voice wavelet frame
transform
),()(2 sfxWs
VVHVHH SSSfP ,2,
Power synthesis over a range / azimuth transect in a linear
basis with orientation ψ
Supervised wavelet statistics analysis
Single look complex slant range polarimetric data
),()(
)(22
4
sfxW
xW
s
s
Wavelet variance
Wavelet kurtosis (flatness factor)
ALOS PALSAR: Hawai’i island Papau Seamount
vvhvhh SSS 2
Flat sea surface
Rayleigh term
Correlation length
White noise
Data delivered by JAXA ALOS PI program
ALOS PALSAR: Hawai’i island Papau Seamount
vvhvhh SSS 2
Sea surface features
1
3
2
Periodicity
Unbounded
Correlation length
Data delivered by JAXA ALOS PI program
ALOS PALSAR: Hawai’i island Papau Seamount
vvhvhh SSS 2
Sea surface features
1
3
2
Maximum shift
Symmetric signature
Local Maxima
Data delivered by JAXA ALOS PI program
A View from Fourier Kingdom
vvhvhh SSS 2
Spectral Characteristics in the H-V Basis
Sea surface featuresVV VV* HH VV* HH HH*
HH HV* HV VV*
HV HV* Xspec(HH HH*,HH HV*)
Xspec(HV HV*,HH HV*)
Xspec(HV HV*,HH HH*)
Flat sea surface Wind waves
Relative differences in energy normalized by HV power
Power Spectrum copol-xpol correlation (HH HV*): 91%
Cross Power Spectrum (Power, Cross) (HH HH*,HV HH*): 95%
Cross Power Spectrum (Power, Power)(HH HH*,HV HV*): 77%
FLATX WIND
X
*
/
HVHV
XXXWINDFLATWIND
Xspec(Power, Crosscor)
Xspec(Power, Power)
Going to Higher Resolution
DLR Tandem-X dual-pol data
Data provided by DLR AO-2010 VEGE0330
Swamp
Lowland
Mosaic
Clear-cut
Lulonga River – Basankuso - DRC
Going to Higher Resolution
DLR Tandem-X InSAR Coherence
Data provided by DLR AO-2010InSAR processing by SARMAP
Swamp
Lowland
Mosaic
Clearcut
CONCLUSIONS
I will not be the same without the jungleCiao, Leb Wohl, Goodbye, Sayonara