1. IGRASS2011
An Interferometric Coherence Optimization Method Based on Genetic Algorithm in PolInSAR
Peifeng Ma, Hong Zhang, Chao Wang, Jiehong Chen
Center for Earth Observation and Digital Earth
Chinese Academy of Sciences
Vancouver, Canada July 29, 2011

2. Outline Introduction to coherence optimization
Present methods for coherence optimization
Cohenrence optimization with genetic algorithm (GA)
Experimental results of GA algorithm
Conclusions

3. Introduction of coherence optimization
Polarimetric SAR
information of the shape, orientation, dielectric properties of scatters
Interferometric SAR
information of location of scatters
Combination of two aspects can be used to estimate
important physical parameters, such as forest height,
extinction coefficient, and topography.

4. Introduction of coherence optimization
scattering matrix:
scattering vector:
generalized vector expression
for the coherence:
The accuracy of height estimation depends on the quality of interferogram, the indicator of which is complex coherence.
We are always attempting to search for the best projection vector combination to acquire the highest interferometric coherence.

5. Present methods Cloude & Papathanassiou algorithm (C&P): Pros:
Two-mechanism algorithm:
Assuming
Cloude & Papathanassiou algorithm (C&P):
By constructing a Lagrangian polynomial for the coherence, we can obtain the
optimum coherence by solution of two different mechanisms.
Pros:
1, optimum solution globally
Cons:
1, introduce polarimetric phase which usually happens in the presence of severe temporal decorrelation
2, instability mathematically

6. Present methods Colin algorithm:
One-mechanism algorithm:
Assuming
Colin algorithm:
By calculating the numerical radius of a matrix, a local maximum can be obtained.
the numerical radius of a matrix A:
Pros:
1, more accurate estimation of phase
Cons:
1, difficult to interpret the second and the third projection vectors physically
2, merely a local optimum solution mathematically

7. Coherence optimization with GA
The fundamental concept of GA is dependent on natural selection in the evolutionary process, including inheritance, mutation, selection and crossover.
Advantages:
more likely converge toward a global optimum
no need of linearization of the problem
more robust
Owing to the merit of capabilities of optimizing globally it is also reasonable to look for the best projection pair using GA to estimate the optimal interferometric coherence

8. Coherence optimization with GA
scattering mechanism definition:
Each individual of population has six chromosomes to be developed in single-mechanism:
When optimizing the second coherence we must add a constraint:
So the last two chromosomes can be represented by the first four as:

9. Coherence optimization with GA
When optimizing the third coherence we must add another constraint:
and
So the last four chromosomes can be represented by the first two as:
where

10. Coherence optimization with GA
Block diagram of coherence optimization using GA:
Pre-processing
Initialization
Genetic operation
Output

11. Optical image from Google Earth and Pauli image
Experiment results
The data we choose is Chinese X-band airborne PolInSAR data over Sanya area:
Optical image from Google Earth and Pauli image

12. Experiment results Initialization: Population size:50
Terminating generation:100
Crossover probability:0.9
Mutation probability:0.1
the interval of :[-1,1]
Precision:0.001
We select one pixel to demonstrate the process of tendency to stability as shown in right.
Initialized and evolutional coherence

13. Experiment results
Mean of coherence in different optimization methods (L=9)
C&P
0.887
0.776
0.602 GA
0.872
0.777
0.622
Colin
0.854
0.791
0.703 GD
0.646
0.481
Histograms of the optimum coherence
The optimum coherence and relative phase

14. Conclusions
Compared with the C&P algorithm, under the control of single-mechanism coherence in GA is more stable without polarimetric phase introduced and hence is more proper to interpret the practical scattering process.
Although the optimum coherence in GA is smaller than that in C&P, the latter two coherences are generally larger because it has larger space when searching the last two coherence.
Compared with other coherences in single-mechanism, the optimum coherence in GA is larger.
Besides, the three projection pairs in GA are absolutely orthogonal and so they can reflect the situation of three orthogonal scattering components in the case of volume scattering.

15. Acknowledgment
This work is supported by National Hi-tech R&D Program of China (Grant No. 2009AA12Z118) and National Natural Science Foundation of China (Grant No and )
East China Electronic Institute is acknowledged for provision of airborne SAR data