1. Meng Liu,Hong Zhang,Chao Wang, Bo Zhang
IGRASS2011
An Analysis of Coherence Optimization Methods in Compact Polarimetric SAR Interferometry
Meng Liu,Hong Zhang,Chao Wang, Bo Zhang
Vancouver, Canada July 29, 2011

2. Coherence Optimization of C-PolInSAR Experiments and Results
Outline 1
Introduction
Coherence Optimization of C-PolInSAR 2
Experiments and Results 3
Conclusions 4

3. Introduction PolInSAR Coherence optimization
PolInSAR uses the interferometric degree of coherence estimated at different polarizations to extend the observation space of targets
Promising applications, especially in the field of forest remote sensing
Coherence optimization
Technique to enhance the interferometric coherence
It is achieved by the choice of a polarization basis within the polarimetric observation space.

4. Introduction Coherence optimization in fully PolInSAR system
Unconstrained Lagrange multipliers method: the potential scattering mechanisms is different in both images
Constrained Lagrange multipliers method: assuming the same scattering mechanism in both images
Numerical radius method: gives a higher coherence than the constrained Lagrange multipliers method

5. Introduction Compact Polarimetry (CP) system
A CP system transmits a wave on π/4 oriented linear or circular polarization, while receives the backward wave on two orthogonal linear or circular polarizations
A CP system has advantage over a fully polarimetric (FP) system in terms of reductions of pulse repetition frequency, data volume, and system power needs

6. Introduction Three modes of CP C-PolInSAR π/4 mode:
Dual Circular Polarimetric mode:
right circular transmit, linear (horizontal and vertical) receive (CTLR) mode:
C-PolInSAR
InSAR CP

7. Introduction The workflow of C-PolInSAR
Simulation
Reconstruction
reconstruction for coherence optimization
Only two independent channels
The assumption: reflection symmetry
insignificance

8. Introduction Objective validation
Solve the coherence optimization problem in C-PolInSAR without the reconstruction of the pseudo F-PolInSAR covariance matrix
validation
Compare coherence optimization of CP modes with the corresponding FP modes, as well as the conventional coherence optimization methods.

9. Coherence Optimization
The complex correlation coefficient of CP
The optimal coherent coefficient
the highest correlation of the two images can be selected by tuning the wi polarization in each resolution element

10. Coherence Optimization
Unconstrained Lagrange multipliers
Solving this equation leads to two 2×2 eigenvalue problems
[A][B] is similar to [B][A], they have the same real nonnegative eigenvalues.

11. Coherence Optimization
Constrained Lagrange multipliers
It assumes the same scattering mechanism in both images
The optimization of the magnitude of the complex correlation leads to one 2×2 eigenvalue problems
This approach take the same polarization basis transformation, which leads to a suboptimum result.

12. Coherence Optimization
Numerical radius
It provides a new thought to solve the constrained Lagrange multipliers function.
Assumption: [T11] is similar to [T22]
Define
The maximum coherence corresponds to the numerical radius of the matrix [A]

13. Experiments and Results
Experimental scene
Test area: Sanya region in China
Acquired: East China Research Institute of Electronic Engineering
Band: X-band
The Pauli decomposition result
Areas
Color
Forest-1 1
Forest-2 2
Crop 3
Road 4
Bare Land 5 1 2 3 4 5

14. Experiments and Results
(a) FP case
The histogram of FP case is right shifted compare to the position of any mode of CP cases
The trend of the coherence histograms for CP case is closed to the corresponding FP case, no matter which method or CP mode was selected
In most cases the ULM gives the highest coherence, followed by the NR and the CLM, this result is similar to the FP case.
(b) π/4 mode
(c) DCP mode
(d) CTLR mode

15. Conventional Coherence
Conventional Coherence VS FP Coherence
ROI
Conventional Coherence
FP Coherence HH HV VV
HH+VV
HH-VV
ULM NR
CLM
forest 1
0.770
0.734
0.780
0.793
0.721
0.913
0.876
0.861
forest 2
0.809
0.774
0.796
0.817
0.750
0.924
0.892
0.870
crop
0.813
0.748
0.797
0.819
0.724
0.931
0.900
0.893
road
0.632
0.382
0.616
0.673
0.509
0.818
0.766
0.751
bare land
0.846
0.707
0.845
0.898
0.635
0.901
0.890
Mean Coherence Values for Compact Polarimetric Modes
ROI
Lin45
DCP
CTLR
ULM NR
CLM
forest 1
0.851
0.830
0.816
0.865
0.843
0.831
0.862
0.839
0.824
forest 2
0.874
0.855
0.836
0.880
0.863
0.845
0.881
0.861
0.846
crop
0.883
0.852
0.887
0.868
0.860
0.866
0.857
road
0.729
0.702
0.681
0.732
0.701
0.683
0.719
0.656
bare land
0.895
0.872
0.893
0.878
0.900
0.870
the degree of coherence for any CP case is lower than the corresponding FP case, but it is higher than the conventional cases.
The HH-VV conventional coherence seems to be the worst case in all case except for the road areas, where the HV conventional coherence is lowest.
Among the three compact modes, the situation becomes complicated. The DCP mode gives the highest coherence over forest 1 and crop areas. For the low forest (forest 2) areas, the CTLR mode is slightly better than other modes.
For the road and bare land areas, the π/4 mode seems to be the best compact mode.

16. Conclusions 1
Compared with the FP case, one can observe that there is a significant loss in coherence of 5-10% when CP modes are available. 2
The trend of the coherence histograms for CP case is closed to the corresponding FP case, no matter which method or CP mode was selected. 3
It is shown that the degree of coherence from CP case carries enough information for some polarimetric SAR interferometry applications.