The document describes methods for tomographic focusing using polarimetric SAR (PolSAR) data, including: 1) A hybrid spectral approach using CAPON and weighted signal subspace fitting to estimate volume boundaries and ground topography from tropical forest data. 2) A single-baseline PolInSAR technique using an RVOG coherence model to retrieve ground elevation and volume coherence from the data. 3) Experimental results applying these methods to P-band PolSAR data collected over tropical forests in Paracou, France.

1. Tomographic focusing Methods Experimental results
Polarimetric SAR Tomography of Tropical
Forests at P-Band
Yue Huang, Laurent Ferro-Famil, Cedric Lardeux
University of Rennes 1, France
July 26, 2011

2. Tomographic focusing Methods Experimental results
Outline
• Introduction
• Methods:
• Proposed Hybrid spectral approach
• Established Single-baseline PolInSAR retrieval technique
• Experimental results over tropical forests, Paracou (P-band)
• Conclusion

3. Tomographic focusing Methods Experimental results
Objectives
In the frame of Biomass estimation of
tropical forests, to estimate:
• Tree height
• Underlying ground topography
MB-PolInSAR: Polarimetric tomography
(PolTomSAR)
• Analyze volume structures
• Separate volume-ground contributions
• Extract physical features

4. Tomographic focusing Methods Experimental results
MB-InSAR data model
Ideal scatterers (D sources)
y(l) = A(z)s(l) + n(l)
A(z) = [a(z1 ), . . . , a(zD )]
Fluctuating scatterers
√
• s(l) = σ x(l) varies over the M
inSAR acquisitions
• Observed signal
• M coherent acquisitions
y = [y1 , . . . , yM ]T D
√
y(l) = σi xi (l) a(zi ) + n(l)
• Steering vector
i=1
a(z) = [1, ejkz2 z , . . . , ejkzM z ]T
• InSAR coherence matrix:
Rii = E(xi (l)xi (l)† )

5. Tomographic focusing Methods Experimental results
MB-InSAR data model
Ideal scatterers (D sources)
y(l) = A(z)s(l) + n(l)
A(z) = [a(z1 ), . . . , a(zD )]
Fluctuating scatterers
√
• s(l) = σ x(l) varies over the M
inSAR acquisitions
• Observed signal
• M coherent acquisitions
y = [y1 , . . . , yM ]T D
√
y(l) = σi xi (l) a(zi ) + n(l)
• Steering vector
i=1
a(z) = [1, ejkz2 z , . . . , ejkzM z ]T
• InSAR coherence matrix:
Rii = E(xi (l)xi (l)† )

6. Tomographic focusing Methods Experimental results
MB-InSAR data model
Ideal scatterers (D sources)
y(l) = A(z)s(l) + n(l)
A(z) = [a(z1 ), . . . , a(zD )]
Fluctuating scatterers
√
• s(l) = σ x(l) varies over the M
inSAR acquisitions
• Observed signal
• M coherent acquisitions
y = [y1 , . . . , yM ]T D
√
y(l) = σi xi (l) a(zi ) + n(l)
• Steering vector
i=1
a(z) = [1, ejkz2 z , . . . , ejkzM z ]T
• InSAR coherence matrix:
Rii = E(xi (l)xi (l)† )

7. Tomographic focusing Methods Experimental results
MB-PolInSAR data model
Single source
• POLSAR unitary target vector
k = [k1 , k2 , k3 ]T , k† k = 1
• Polarimetric steering vector
a(z, k) = k ⊗ a(z)
• 3-M element MB-POLinSAR signal
 
y1 (l)
yP (l) =  y2 (l)  = s(l)a(z, k) + n(l)
y3 (l)
D sources
• Polarimetric steering matrix
A(z, K) = [a(z1 , k1 ), . . . , a(zD , kD )]
• 3-M element MB-POLinSAR signal
yP = A(z, K)s + n

8. Tomographic focusing Methods Experimental results
MB-PolInSAR data model
Single source
• POLSAR unitary target vector
k = [k1 , k2 , k3 ]T , k† k = 1
• Polarimetric steering vector
a(z, k) = k ⊗ a(z)
• 3-M element MB-POLinSAR signal
 
y1 (l)
yP (l) =  y2 (l)  = s(l)a(z, k) + n(l)
y3 (l)
D sources
• Polarimetric steering matrix
A(z, K) = [a(z1 , k1 ), . . . , a(zD , kD )]
• 3-M element MB-POLinSAR signal
yP = A(z, K)s + n

9. Tomographic focusing Methods Experimental results
Objectives of PolTomSAR focusing
Discrete case (Ns sources) Continuous case
• Heights: ˆ
z • Reflectivity: σ (z)
ˆ
• Reflectivities: σ
ˆ • Polarimatric mech.:
• Polarimatric mech.: k(z)
ˆ
K
Practical implementation
• Parameters estimated from
ˆ 1 L ˆ 1 L
SP: R = L l=1 y(l)y(l)† FP: R = L l=1 yp (l)yp (l)†
• Ns : estimated using Model Order Selection techniques

10. Tomographic focusing Methods Experimental results
Conventional tomographic estimators
Nonparametric estimators
Capon:
1
σ (z) =
ˆ
ˆ
aH R−1 a
• Continuous spectrum, moderate resolution
Parametric estimators
Weighted Signal Subspace Fitting (SSF):
ˆ ˆs
ˆ = arg max tr{PA Es WEH }
z
PA projection matrix of A, Es signal subspace
• Discrete spectrum, high resolution
Lack of adaptation to the type of spectrum!

11. Tomographic focusing Methods Experimental results
Proposed hybrid spectral approach
Objective: Very fast estimation of the boundaries of a volumic
medium
• CAPON
Backscattered power spectrum P(z)
• SSF (order=2)
Ground topography zg
Phase center of the volume zv
• Tree top height:
ztop = {z|P(z) = P(zv )-3dB}
Easy extended to polarimetric case.

12. Tomographic focusing Methods Experimental results
Single-baseline PolInSAR retrieval technique
• RVOG coherence line model* γ(ω)
(*Cloude and Papathanassiou, 2003)
• Analytic method: Matrix Least-Squares estimator*
(*Ferro-Famil et al. 2009):
ˆ
• Ground phase φg ⇐ Pc1 , Pc2
• Volume coherence γv ⇐ γM , γm
ˆ
• Inversion:
ˆ
φg
• Ground elevation: Hg = kz
ˆ
arg(γv e−j φg )
• DEM differencing: Hv = kz

13. Tomographic focusing Methods Experimental results
Presentation of test sites
• TropiSAR Campaign, 2009
• ONERA SETHI
• P-Band
• 6 tracks
• δaz = 1.245m
δrg = 1m
• δz = 12.5m
Ground truth
• LiDAR measurements Courtesy ONERA
• Biomass measurements

14. Tomographic focusing Methods Experimental results
Presentation of test site: Paracou
Optical image SAR image LiDAR zg LiDAR ztop
• Tropical forest environments
• Highly varying ground topography
(savannah, undisturbed forests, logged plots...)

15. Tomographic focusing Methods Experimental results
SB PolInSAR retrieval technique
• Underlying ground zg : overestimated

16. Tomographic focusing Methods Experimental results
Proposed hybrid spectral approach
• Estimated profiles match LiDAR
• HH profiles: similar to FP case
HH
HV FP

17. Tomographic focusing Methods Experimental results
LiDAR data (slant range) zg , ztop Hv
zg ztop Hv
Estimated results (slant range)
ˆ
zg ˆ
ztop ˆ
Hv

18. Tomographic focusing Methods Experimental results
Geometry of tree height measurements
ˆ
Tree height: Hv = ztop − zg
Projection of zg , ztop in ground range is required!

19. Tomographic focusing Methods Experimental results
LiDAR data (ground range) zg , ztop Hv
zg ztop Hv
Estimated results (ground range)
ˆ
zg ˆ
ztop ˆ
Hv

20. Tomographic focusing Methods Experimental results
zg ztop Hv
TomSAR-LiDAR [m] Mean Std
∆zg 0.005 4.6
∆ztop 1.6 7.4
∆Hv 0.9 7.7

21. Tomographic focusing Methods Experimental results
ROI Distribution
No. Type Biomass (T/ha)
in 2007
P9 Logged plots (T1 ) 359.6
P10 Logged plots (T2) 318.0
P11 Undisturbed forest 428.5
P12 Logged plots(T3) 318.2
• T1: exploitation of timbers
• T2: exploitation of timbers + removal of
non-commercial species
• T3: exploitation of timbers + exploitation
of commercial species + removal of
non-commercial species

22. Tomographic focusing Methods Experimental results
P9 P10
Lidar measurements Hv
mean=28.2m mean=26.6m
Estimated Hv
mean=28.9m mean=27.7m

23. Tomographic focusing Methods Experimental results
P11 P12
Lidar measurements Hv
mean=29.5m mean=26.6m
Estimated Hv
mean=31.3m mean=27.3m

24. Tomographic focusing Methods Experimental results
Conclusion
Tropical forests characterization
• Single baseline PolInSAR method:
overestimates the underlying ground topography
• Hybrid spectral approach:
HH similar to FP
provides very good estimate for zg and ztop of tropical forests.
Estimated quantities are validated against LiDAR data.