2 A Bouvet 1 European Commission Joint Research Centre 21027 Ispra VA Italy email frankdegrandijrceceuropaeu Twopoint statistic of polarimetric SAR data provided by a wavelet frame ID: 1025064
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1. G. F. De Grandi1, R.M. Lucas2, A. Bouvet1European Commission Joint Research Centre21027, Ispra (VA), Italye-mail: frank.de-grandi@jrc.ec.europa.euTwo-point statistic of polarimetric SAR data provided by a wavelet frameThe importance of being scaling…(suggested by Oscar Wilde)Institute of Geography and Earth SciencesAberystwyth University, Aberystwyth, UK, SY23 3DB.e-mail: rml@aber.ac.uk
2. Bits of History
3. Problem StatementTwo-point statistic provided by wavelet coefficientsStructure FunctionWavelet VarianceSpatial random field (SRF)Wavelet frame transform
4. What happens when the polarization basis is changed?Wavelet variance of 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 processHj Fourier transform of the wavelet dilated at scale j ACF of wavelet coefficients computed in the frequency domain from the power spectrum G of the input processWavelet variance at cross-polarized state with orientation ψWavelet transformPower spectrum inPower spectrum out
6. Power spectrum of the crosspolar power in the rotated basis Rotation to a linear basis with orientation ψCross-polarized component in the new basis ψ
7. Power spectrum of the input process 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 basisCopol-xpol correlationPower-CorrelationHV2HH2, VV2
8. A numerical model for the wavelet variance of a correlated K-distributed stationary clutter The Wavelet Scaling Polarimetric Signature (WASPS)Correlated K-distributed clutter, C. Oliver
9. From theory to practice Multi-voice wavelet frame transformPower synthesis over a range / azimuth transect in a linear basis with orientation ψSupervised wavelet statistics analysisSingle look complex slant range polarimetric dataWavelet varianceWavelet kurtosis (flatness factor)
10. ALOS PALSAR: Hawai’i island Papau Seamount Flat sea surfaceRayleigh termCorrelation lengthWhite noiseData delivered by JAXA ALOS PI program
11. ALOS PALSAR: Hawai’i island Papau Seamount Sea surface features132PeriodicityUnboundedCorrelation lengthData delivered by JAXA ALOS PI program
12. ALOS PALSAR: Hawai’i island Papau Seamount Sea surface features132Maximum shiftSymmetric signatureLocal MaximaData delivered by JAXA ALOS PI program
13. A View from Fourier Kingdom Spectral Characteristics in the H-V BasisSea 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 surfaceWind wavesRelative 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% Xspec(Power, Crosscor)Xspec(Power, Power)
14. Going to Higher Resolution DLR Tandem-X dual-pol dataData provided by DLR AO-2010 VEGE0330 SwampLowlandMosaicClear-cutLulonga River – Basankuso - DRC
15. Going to Higher Resolution DLR Tandem-X InSAR CoherenceData provided by DLR AO-2010InSAR processing by SARMAP SwampLowlandMosaicClearcut
16. CONCLUSIONS I will not be the same without the jungleCiao, Leb Wohl, Goodbye, Sayonara