TWO-POINT STATISTIC OF POLARIMETRIC SAR DATA TWO-POINT STATISTIC OF POLARIMETRIC SAR DATA
1. Two-point statistic of polarimetric SAR data provided
by a wavelet frame
The importance of being scaling…(suggested by Oscar Wilde)
G. F. De Grandi1, R.M. Lucas2, A. Bouvet1
European Commission Joint Research Centre Institute of Geography and Earth Sciences
21027, Ispra (VA), Italy Aberystwyth University, Aberystwyth, UK,
e-mail: frank.de-grandi@jrc.ec.europa.eu SY23 3DB.
e-mail: rml@aber.ac.uk
3. Problem Statement
T Two-point statistic
Shh 2Shv Svv Wavelet frame provided by wavelet
transform coefficients
Shv *
Phv ( Shh y )2Shv SvvShv ( x , y )
x,
Wavelet
Variance
w2 ( x) f ( scale )
Structure Function
Spatial random field
2
(SRF) f( ) f ( x) f (x )
4. What happens when the polarization basis is changed?
T ' sin 2
Shh 2Shv Svv T
1 cos 2
Shh 2Shv Svv
xpol ' '*
P ( x, y, ) 2 2 ( x, y, )
copol ' '*
P ( x, y, ) 1 1 ( x, y, )
2 Wavelet variance of
w ( x) f( , ) the crospolar and
copolar power in the
rotated polarization
basis
5. Wavelet variance of PolSAR power in a rotated basis: a
model for a WS stationary process
Wavelet Power
Power
transform spectrum out
spectrum in
Shh 2Shv Svv
G Hj Gout
in
Hj Fourier transform of the wavelet dilated at scale j
1 2 ACF of wavelet coefficients computed
Rout Gin Hj in the frequency domain from the
power spectrum G of the input process
Wavelet variance at cross-polarized
w i2 R out 0 state with orientation ψ
6. Power spectrum of the crosspolar power in the rotated basis
S HH , 2S HV , S VV S c1 Sc1
HV
c22 SVV 2 S HH
cos
Shh 2Shv Svv 2
Rotation to a linear basis with
orientation ψ
c2 in the new basis ψ2
sin
Cross-polarized component
2
2 * *
Pab ( ) c Si S
i i ci c j Re Si S j
i ij
Si S HH , S HV , SVV
Pab ( ) ai X i
i
7. HV2
Copol-xpol
Power spectrum of the input process
correlation2 HH , VV2
Power-
Correlation
2 * *
Pab ( ) c Si S
i i ci c j Re S i S j
i ij
Pab ( ) ai X i
i
*
G ( ) a X a
Power spectrum in the rotated basis is a linear combination jof the
in i i j X
i j
power spectra (auto-correlation) and cross-spectra (cross
correlation) between dyads of the vector in the H,V basis
2
G ( )
in
aG i Xi
aaG i j Xi ,X j
i ij
8. A numerical model for the wavelet variance of a
correlated K-distributed stationary clutter
The Wavelet Scaling Polarimetric
Signature (WASPS)
w2 ( x) f( , )
Shh 2Shv Svv
Correlated K-distributed
clutter, C. Oliver
9. From theory to practice
Supervised wavelet statistics analysis
Single look complex slant range
polarimetric data
Shh 2Shv Svv
2
W ( x) s f ( s, )
Wavelet variance
Multi-voice
4
Power synthesis over a range /
wavelet frame
transform
W ( x)
s
azimuth transect in a linear
2
f ( s, )
basis with orientation ψ 2
W ( x)
s
P f S HH , 2 S HV , SVV
Wavelet kurtosis
(flatness factor)
10. ALOS PALSAR: Hawai’i island Papau Seamount
Flat sea surface
Data delivered by JAXA
ALOS PI program
Correlation White
Shh 2Shv Svv length noise
Rayleigh
term
11. ALOS PALSAR: Hawai’i island Papau Seamount
3
Sea surface features
Data delivered by JAXA
ALOS PI program
Shh 2Shv Svv Unbounded
Periodicity
Correlation
length
2
1
12. Data delivered by JAXA
ALOS PI program ALOS PALSAR: Hawai’i island Papau Seamount
Local
Maxima Sea surface features
3
Maximum
shift
Shh 2Shv Svv
Symmetric
signature
2
1
13. A View from Fourier Kingdom
Spectral Characteristics in the H-V Basis
Sea surface features
VV VV* HH VV* HH HH*
HH HV* HV VV*
HV HV*
Shh 2Shv Svv Xspec(HH HH*,HH HV*)
Xspec(Power, Crosscor)
Xspec(HV HV*,HH HH*)
Xspec(HV HV*,HH HV*)
Xspec(Power, Power)
Flat sea surface X FLAT
Wind waves X WIND
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%
X WIND
X /X
FLAT WIND
*
Cross Power Spectrum (Power, Power)(HH HH*,HV HV*): 77% HV HV
14. Going to Higher Resolution
DLR Tandem-X dual-pol data
Lulonga River – Basankuso - DRC
Data provided by DLR AO-2010 VEGE0330
Swamp
Mosaic
Lowland
Clear-cut
15. Going to Higher Resolution
DLR Tandem-X InSAR Coherence
Data provided by DLR AO-2010
InSAR processing by SARMAP
Swamp
Mosaic
Lowland
Clearcut