The document describes a random volume over ground (RVoG) coherent scattering model for polarimetric SAR interferometry (PolInSAR) data. It presents the RVoG model equations relating the volume and ground contributions to the PolInSAR coherency matrix. It then shows how to separate the volume and ground scattering contributions based on the model and retrieve the interferometric phases. Finally, it discusses validation of the model using both simulated and experimental X-band PolInSAR data.

1. López-Martínez, P. Papathanassoiu, Alonso-
Carlos López Martínez Kostanstinos P Papathanassoiu Alberto Alonso
González , Xavier Fàbregas,
IGARSS-2011 Universitat Politècnica de Catalunya – UPC
German Aerospace Center - DLR
Signal Theory and Communications Department – TSC
Microwaves and Radar
July-2011 Remote Sensing Laboratory - RSLab., Barcelona, Spain
Institute –HR, Wessling, Germany
Vancouver (BC), Canada carlos.lopez@tsc.upc.edu

2. Outline
RVoG coherent scattering model
Separation of scattering contributions
Retrieval of interferometric information
Validation based on Simulated PolInSAR data
Validation based on Experimental X-band PolInSAR data
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 2 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

3. Polarimetric SAR Interferometry
Random Volume over Ground RVoG coherent scattering model
g
 Τ11 Ω12 
Τ6   
Ω 21 Τ22 
Topo. phase
1 : topo. phase PolInSAR
coherency matrix
2 : canopy bottom
phase
PolSAR information
2 hv 2 hv hv 2 z  hv 2 z 
 
Τ11  Τ22  I  ev
1
cos0
I g
1 I e
v
1
cos 0
e
cos0
Τv d 
dz I     z e
g
1
cos0
Τg d   Τg
dz
0 0
PolInSAR information
2 hv 2 hv hv 2 z  hv 2 z 
 
Ω12  e j2 I v  e j1 e
2
cos0 g
I2 Iv  e
2
cos0
e
j z z  cos 0
e Τv dz  I 2     z e
g cos0
Τ g dz   Τ g
0 0
1 0 0  1 t12 0
Volume Τv  mv 0  0 
 Ground Τ g  mg t12 t22

0 
contribution  contribution 
0 0  
   0 0 t33 

Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 3 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

4. Polarimetric SAR Interferometry
Interferometric coherence under the hypothesis of the RVoG model
Topo. phase
H
w Ω 12 w   m w  sol. #2
 w    e j1 v 1
w H Τ11w 1  m w  v w
mg  w 
m w   1
mv  w  I 0 Topo. phase
sol.
sol #1
Ground-to-volume ratio
hV
 2 z ' 
I   e jz z ' exp   dz '
I  cos0 
v  0
I0 hV
 2 z ' 
I0   exp  No direct access neither to the
 dz '
0  cos0  underneath topography nor the volume
Volume coherence
coherence due to the limitation on the
visible line length of the linear
dependency of the interferometric

z  coherence w.r.t. th polarization state
h t the l i ti t t
sin(0 )
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 4 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

5. PolInSAR Complex Correlation Coefficient
In the most g
general case, the complex correlation coefficient is defined in terms of
, p
two generalized scattering mechanisms
H
w 1 Ω12 w 2
  w1, w 2  
H H
w 1 Τ11w 1w 2 Τ 22 w 2
Assumption of the RVoG model
H
w 1 Ω 12 w 2
  w1 , w 2  
H H
w 1 Τ11w 1w 2 Τ11 w 2
2  hv
 j v j1

cos  0 g

w1  e I 2  e e
H 2
I2  w 2
 
  w1 , w 2    
2  hv 2  hv
 v 
cos  0 g
  v 
cos  0 g

w 1  I1  e
H
I1  w 1w 2  I1  e
H
I1  w 2
   
   
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 5 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

6. PolInSAR Complex Correlation Coefficient
Separation, in terms of the numerator, of the complex correlation coefficient, under
p , , p ,
the assumption of the RVoG coherent scattering model
  w1 , w 2   v  w1 , w 2    g  w1 , w 2 
Volume contribution
e j2 w1 I v w 2
H
 v  w1 , w 2   2
2 h 2 h
 v  cosv g   v  cosv g 
w1  I1  e
H 0
I1  w1w 2  I1  e
H 0
I1  w 2
   
   
Ground (double bounce) contribution
2 hv

cos0
e j1 e H g
w1 I 2 w 2
 g  w1 , w 2  
2 h 2 h
 v  cosv g   v  cosv g 
w1  I1  e
H 0
I1  w1w 2  I1  e
H 0
I1  w 2
   
   
Cancelation, in terms of the numerator, of one of the previous components
w1 , w 2 that cancel the volume or the ground contribution
g
w1 , w 2 that cancel one component while maximizing the other one
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 6 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

7. Cancelation of the Volume Component
Volume component can be cancelled considering
p g
1 0 0 
e j2 mv Cv w1 0  0  w 2  0
H
 
e j2 w1 I v w 2  0
H 0 0  
 
2
2 hv hv 2 z 
Cv  e cos 0
e
j z z  cos0
e dz  where: arg Cv   arg   v 
0
Cancellation can be independent of the volume properties
1 0 0   w21 
  w11w21  0
*
w

*
w *
w13  0  0   w22   0
*
 
11 12
w12 w22  w13 w23  0
* *
0 0    w23 
  
Optimization of the ground component maximize   w1 , w 2 
can be considered subject to w11w21  0
*
w12 w22  w13 w23  0
* *
w1 Τ11w1  ct
H
t
w 2 Τ11w 2  ct
H
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 7 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

8. Cancelation of the Ground Component
Ground (double bounce) component can be cancelled considering
( ) p g

2 hv 2 hv 1 t12 0

mg w1 t12 0  w2  0
cos0
e j1 e w1 I 2 w 2  0
H g
e j1 e cos0 H 
t22
 
0
 0 t33 

Cancelation is performed using different normalized eigenvectors of the
g
ground scattering matrix
g
T
t  t   t11  t22   4 t12
2 2 
wa   1 0
11 22
 *
2t12 
 
T
t  t   t11  t22 
2
 4 t12
2 
wb   1 0
11 22
 2t *
12

 
w c   0 0 1
T
The third eigenvector can not be considered as it is also an eigenvector
of the volume scattering matrix
Estimation of the ground contribution necessary
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 8 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

9. Phase Component Analysis
Volumetric and ground contributions have been separated, but the phase component
g p , p p
of the remaining coherence terms presents polarimetric and interferometric
contributions
2 hv 2 hv Cv mv e j  mg mg t12 0 

cos0

cos0  
Ω12  e j1 e Ω12  e j1 e
 
*
mg t12 Cv mv e j  mg t22 0 
 0 0 Cv mv e j  mg t33 
 
Under the basis that w1 and w2 cancel the volume contribution of coherence
arg w 2 Ω12 w1    arg w1 Ω12 w 2 
H
 H

Under the basis that w1 and w2 cancel the ground contribution of coherence
w1 Ω12 w 2  Cv  w11w21   w12 w22   w13 w23   Cv w
H * * *
w 2 Ω12 w1  Cv  w21w11   w22 w12   w23 w13   Cv w*
H * * *
These properties will allow to remove polarimetric information from phase
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 9 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

10. Cancelation of the Volume Component
Assuming the cancelation of the volume contribution in coherence
g
2 h
 j  cosv H
 1 

arg w1 Ω12 w 2   arg e e
H 0
 w 2   1  arg w1 Ω12 w 2 
w1 Ω12 H


 

2 h
 j  cosv H
 1 

arg w 2 Ω12 w1   arg e e
H 0
w 2 Ω12 w1   1  arg w 2 Ω12 w1   1  arg w1 Ω12 w 2 
 H
 H


 

A non biased estimation of the underlying ground topography on vegetated areas is
non-biased
obtained through the analytical expression
1
1  arg w1 Ω12 w 2  w 2 Ω12 w1 
g H H
2
Generalization of previous results
1
EUSAR 2010 (Aachen, Germany) 1  arg Ω12 1, 2  Ω12  2,1
2
IGARSS 2010 (Honolulu, USA) 1  arg Ω12 1, 2  T11  2,1
C. López-Martínez and K. P. Papathanassiou, “Cancelation of Scattering Mechanisms in
PolInSAR: Application to Undelying Topography Estimation,” Submitted to IEEE TGRS
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 10 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

11. Cancelation of the Ground Component
Assuming the cancelation of the g
g ground contribution in coherence
w1 Ω12 w 2  Cv  w11w21   w12 w22   w13 w23   Cv w
H * * *
w 2 Ω12 w1  Cv  w21w11   w22 w12   w23 w13   Cv w*
H * * *
e j2 w1 I v w 2
H
 v  w1 , w 2   2
2 h 2 h
 v  cosv g   v  cosv g 
w1  I1  e
H 0
I1  w1w 2  I1  e
H 0
I1  w 2
   
   
A non-biased estimation of the interferometric phase associated to the volume
non biased
scattering center on vegetated areas is obtained through the analytical expression
2 hv

cos 0 2
e j 22 w1 Ω12 w 2  w 2 Ω12 w1  e j 22 e
H H
Cv2 w
1
arg Cv   arg e j 22 w1 Ω12 w 2  w 2 Ω12 w1   2
H H
2
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 11 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

12. Validation Based on Simulated Data
Underlying topography estimation 1
y g p g p y Speckle noise effects
p
considering hv=20 m and η=0.1 0.5
 3 3
0 0
Mean  [rad]
4 8 4
12000
1
-0.5
9x9 MLT -1
10000 -1.5
2 4 6 8 10 12 14 16
Mlt size [size]
8000 1 =0 rad
# counts
2
6000
1.5
Mean  [rad]
1
4000
1
0.5
0
2000 -0.5
2 4 6 8 10 12 14 16
Mlt size [size]
0
-2
2 0 2 1 =3π/8 rad
3π/8
angle [rad]
Unbiased estimation of the ground
topography on vegetated areas
p g p y g
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 12 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

13. Validation Based on Simulated Data
Estimation of the interferometric phase
p Speckle noise effects
p
associated to the volumetric scattering -0.1
center arg{Cv} and η=0.1
Mean arg{C } [rad]
-0.2
4 -0.3
v
x 10
-0.4
0.4
a
2 h =5 m
-0.5
v -0.6
2 4 6 8 10 12 14 16
h =10 m Mlt size [size]
v
1.5 h =15 m
v
hv =10 m
# counts
h =20 m 0
v
Mean arg{C } [rad]
1 -0.5
v
9x9 MLT
a
-1
0.5
-1.5
2 4 6 8 10 12 14 16
Mlt size [size]
0 hv =20 m
20
-1.5 -1 -0.5 0 0.5 1 1.5
angle [rad]
Unbiased estimation of the
volumetric scattering center phase
g p
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 13 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

14. Results: Experimental X-band PolInSAR Data
Underlying topography estimation: X-band experimental PolInSAR data
X band
TanDEM-X Feb 2011
X band Dual-Pol
X-band Dual Pol data: HH&VV
Bistatic cooperative mode
Effective spatial baseline: 39.22 m
Single pass acquisition
Incidence angle (scene center): 33.78º
Height of ambiguity: 134.46 m
kz: 0.0467 rad/m
Boreal Forest
Snow depth (Folköping ski resort):
25 – 80 cms
Temperature (5:32am): -25º
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 14 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

15. Results: Experimental X-band PolInSAR Data
X-
Forest areas that have been considered
|VV1| |VV2|
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 15 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

16. Results: Experimental X-band PolInSAR Data
X-
Polarimetric information content
Scene 1 Scene 2
|C11| |C11-2Re{C12}+C22|
|C11 2Re{C12}+C22| |C22|
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 16 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

17. Results: Experimental X-band PolInSAR Data
X-
PolSAR information content of Scene 1
Master image
PolInSAR information content
Master/Slave int.
|r(HH1+VV1,HH1-VV1)| |–(HH1+VV1,HH1-VV1)|
Slave image
|r(HH1 VV1 HH2 VV2)|
(HH1+VV1,HH2-VV2) |–(HH1 VV1 HH2 VV2)|
(HH1+VV1,HH2-VV2)
Coherence
0 1
Phase
Ph
-180 180
|r(HH2+VV2,HH2-VV2)| |–(HH2+VV2,HH2-VV2)|
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 17 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

18. Results: Experimental X-band PolInSAR Data
X-
PolSAR information content of Scene 1
Master image Dual-PolSAR data eigendecomposition
Entropy α
0 1 0 90
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 18 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

19. Results: Experimental X-band PolInSAR Data
X-
PolSAR information content of Scene 2
Master image
PolInSAR information content
Master/Slave int.
|r(HH1+VV1,HH1-VV1)| |–(HH1+VV1,HH1-VV1)|
Slave image
|r(HH1 VV1 HH2 VV2)|
(HH1+VV1,HH2-VV2) |–(HH1 VV1 HH2 VV2)|
(HH1+VV1,HH2-VV2)
Coherence
0 1
Phase
Ph
-180 180
|r(HH2+VV2,HH2-VV2)| |–(HH2+VV2,HH2-VV2)|
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 19 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

20. Results: Experimental X-band PolInSAR Data
X-
PolSAR information content of Scene 2
Master image Dual-PolSAR data eigendecomposition
Entropy α
0 1 0 90
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 20 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

21. Results: Experimental X-band PolInSAR Data
X-
Ground topography estimation on Scene 1
p g p y
Due to penetration properties at X-band, the estimated phase center could
be considered as the lowest phase center, not the ground topography phase
center
Forest Lake
1  arg Ω12 1, 2  T11  2,1 f RPh=|–(HH1+VV1,HH2+VV2)| Phase difference Δf=f1- f RPh
(HH1 VV1,HH2 VV2)
Reference phase
(Highest phase center) Lake: E{Δf} = 0.18 rad
E{Δh} = 3.83 m
-180 180
|C11| Forest: E{Δf} = -0 19 rad
0.19
E{Δh} = -4.16 m
|C11-2Re{C12}+C22|
|C22|
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 21 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

22. Results: Experimental X-band PolInSAR Data
X-
Ground topography estimation on Scene 2
p g p y
Forest 1 Forest 2
1  arg Ω12 1 2  T11  2,1
1, 21 f RPh=|–(HH1+VV1,HH2+VV2)|
|– difference Δf=f1- f RPh
Phase diff
Ph
Reference phase
(Highest phase center)
Forest 1: E{Δf} = -0.08 rad
E{Δh} = -1 71 m
1.71
-180 180
Forest 2: E{Δf} = -0.05 rad
E{Δh} = -1.04 m
|C11|
|C11-2Re{C12}+C22|
|C22|
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 22 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

23. Conclusions
Extended analysis of the RVoG coherent scattering model for forested areas
y g
characterization
Use of orthogonal scattering mechanisms allows to separate different polarimetric
scattering mechanisms
Low coherence problem
Direct, unbiased & unambiguous estimation of the underlying topography and the
volumetric phase scattering center
Analytical expression for the underlying topography
Asymptotically unbiased estimation from an stochastic point of view
Results validated with P-band data
Results with X-band PolInSAR
Presence of penetration in forests at X-band in the order of 1 to 5 meters
Assumption of the RVoG at X-band
Results subjected to the presence of a snow cover on the analyzed data
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 23 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

24. Simulated PolInSAR Data
Underlying topography estimation: Simulated PolInSAR data
Simulated scenario: Forest under the hypothesis of the RVoG model
Forest, η=0.25, σ=0.3 dB/m
Variable hv
μ=-5 dB
Flat, rough, loamy terrain,
2.2%
2 2% water content (X-Bragg)
Variable ground phase
Imaging systems: DLR s E-SAR
DLR’s E SAR
Range spatial resolution 1.5 m
Azimuth spatial resolution 1.5 m
Wavelength λ=0 23 m (L-band)
λ=0.23
Flight height H=3000 m
Mean incidence angle θ=45 deg
Horizontal baseline B=5 m
Statistical distribution: Wishart pdf
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 24 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

25. Validation
Cancelation of the volume coherence and optimization of the ground coherence
p g
Numerical optimization procedure
1 0.2
0.8 0.15
0.6
0.1
| |
| |
0.4
0.05
0.2
0 0
0 10 20 30 40 50 0 10 20 30 40 50 60 70 80
Iteration
η=0 4
Iteration
η=0.25
4
2 2
angle(  )
angle(  )
0 0
-2 -2
-4 -4
0 10 20 30 40 50 0 10 20 30 40 50 60 70 80
Iteration Iteration
0.5
0.4
0.3 |(w1 ,w2 )|
| |
0.2
|v (w1 ,w2 )|
0.1
0
0 10 20 30 40 50 60 70 80 90
|g(w1 ,w2 )|
Iteration
η=0.5
angle((w1 ,w2 ))
4
2
angle(v (w1 ,w2 ))
angle  )
e(
0
-2
angle(g(w1 ,w2 ))
-4
0 10 20 30 40 50 60 70 80 90
Iteration Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 25 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

26. Validation
Cancelation of the ground coherence
g
The actual ground scattering matrix is considered
η is provided
The ground scattering matrix is estimated from data
η is provided
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 26 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

27. Results: Experimental PolInSAR Data
Underlying topography estimation: P-band experimental PolInSAR data
P band
INDREX-II campaign Oct-Dec 2004
Observation system: DLR E-SAR
P-band data
ba d
Spatial baselines B: 15 m, 30 m
Temporal baselines T: 20 min, 40 min
Tropical forest
Mawas-E site, Central Kalimantan, Indonesia
Flat area
Tropical peat swamp forest types
Bi
Biomass range: 50 400 t /h
50-400 ton/ha
Height range: 5-25 m
Pauli RGC decomposition of the master data set |HH+VV| |HV| |HH-VV| Aerial photograph
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 27 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

28. Results: Experimental PolInSAR Data
Dataset: P-band, B=15 m
,
Transformation to height [m] information included (κz)
Height retrieved from 1
Phase center 
S hv ,1S hv ,2
height retrieved from
Height difference
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 28 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

29. Results: Experimental PolInSAR Data
Dataset: P-band, B=30 m
,
Transformation to height [m] information included (κz)
Height retrieved from 1
Phase center 
S hv ,1S hv ,2
height retrieved from
Height difference
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 29 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

30. Results: Experimental PolInSAR Data
Underlying topography estimation: Absolute height analysis
y g p g p y g y
Height retrieved from 1 B = 15 m 
Height retrieved from Shv ,1S hv ,2
Forest Un-vegetated Forest/Low vegetation
25
 1 (B=15m)
20 *
Ph. <Shv,1Shv,2> (B=15m)
15  1 (B=30m)
*
Ph. <Shv,1Shv,2> (B=30m)
Height [m]
10
[
5
0
-5
-10
3000 3200 3400 3600 3800 4000 4200 4400 4600
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu # pixel 30 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya

31. Results: Experimental PolInSAR Data
Underlying topography estimation: Height difference analysis
y g p g p y g y
B = 15 m
Area 1
4
x 10
4
B = 15 m
3.5 B = 30 m Area 2
3 Area 1 mean value = - 0.57 m
2.5
Area 2 mean value = 7 48 m
A l 7.48
# counts
2
1.5
1
B = 30 m
0.5
Area 1
0
-20 -10 0 10 20
Height dif [m]
Area 2
Area 1 mean value = - 0.32 m
Area 2 mean value = 6.83 m
Remote Sensing Lab.
© Carlos López-Martínez, 2011, UPC-RSLab, carlos.lopez@tsc.upc.edu 31 Signal Theory and Communications Dept.
Universitat Politècnica de Catalunya