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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 EarthChinese Academy of Sciences
Vancouver, Canada July 29, 2011
IGRASS2011
Outline
Introduction to coherence optimizationPresent methods for coherence optimization Cohenrence optimization with genetic
algorithm (GA)Experimental results of GA algorithmConclusions
Polarimetric SARinformation 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.
Introduction of coherence optimization
Introduction of coherence optimization
scattering matrix: scattering vector:[ ]S1
[ , , 2 ]2
THH VV HH VV HVk S S S S S
*1 12 2
* *1 11 1 2 22 2
T
T T
T
T T
*12 1 2[ ] TT k k*
11 1 1[ ] TT k k *22 2 2[ ] TT k k
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.
Present methods
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.
Cons:1, introduce polarimetric phase which usually happens in the presence of severe temporal decorrelation2, instability mathematically
Pros:1, optimum solution globally
* * *1 12 2 1 1 11 1 1 2 2 22 2 2( ) ( )T T TL T T C T C
Two-mechanism algorithm: 1 2 Assuming
Present methods
Colin algorithm: By calculating the numerical radius of a matrix, a local maximum can be obtained.
Cons:1, difficult to interpret the second and the third projection vectors physically2, merely a local optimum solution mathematically
*( ) max{ : , 1}A x Ax x C x
the numerical radius of a matrix A:
Pros:1, more accurate estimation of phase
One-mechanism algorithm: 1 2 Assuming
Coherence optimization with GA
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
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
Coherence optimization with GA
scattering mechanism definition:
*( 1 2, 3 4, 5 6) Tv iv v iv v iv
Each individual of population has six chromosomes to be developed in single-mechanism: [ 1 6]v v
When optimizing the second coherence we must add a constraint:*
1 2 0Topt opt
So the last two chromosomes can be represented by the first four as:4
1 1 25
1 2 1 2 1 2 1 212 1 1 2 4 3 3 41
2 65 1 1
1 5 56 1
6
1 2 1 2 1 2 1 2 1 22 1 1 2 2 3 3 4 4 5 56 1
5
( )
opt opt opti i
opt opt opt opt opt opt opt optiopt
optopt opt
optopt
opt opt opt opt opt opt opt opt opt optopt
opt
v v vv v v v v v v v
vv
v vv
v
v v v v v v v v v vv
v
Coherence optimization with GA
*1 2 0Topt opt
When optimizing the third coherence we must add another constraint:*
2 3 0Topt opt and
So the last four chromosomes can be represented by the first two as:
3 1 1 1 13 3 4 5 6
3 1 1 1 14 4 3 6 5
3 2 2 2 25 3 4 5 6
3 2 2 2 26 4 3 6 5
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
opt opt opt opt opt
opt opt opt opt opt
opt opt opt opt opt
opt opt opt opt opt
v v R v R v R v R
v v R v R v R v R
v v R v R v R v R
v v R v R v R v R
1 3 1 31 1 2 2
1 3 1 31 2 2 1
2 3 2 31 1 2 2
2 3 2 31 2 2 1
1
2
3
4
opt opt opt opt
opt opt opt opt
opt opt opt opt
opt opt opt opt
R v v v v
R v v v v
R v v v v
R v v v v
where
Coherence optimization with GA Block diagram of coherence optimization using GA:
Pre-processing Initialization
Genetic operation
Output
Experiment results
The data we choose is Chinese X-band airborne PolInSAR data over Sanya area:
Optical image from Google Earth and Pauli image
Experiment results
Initialization:Population size:50Terminating generation:100Crossover probability:0.9Mutation probability:0.1the interval of :[-1,1]Precision:0.001
We select one pixel to demonstrate the process of tendency to stability as shown in right.
i
i
Initialized and evolutional coherence
Experiment results
C&P 0.887 0.776 0.602
GA 0.872 0.777 0.622
Colin 0.854 0.791 0.703
GD 0.776 0.646 0.481
1opt 2opt3opt
Mean of coherence in different optimization methods (L=9)
The optimum coherence and relative phase
Histograms of the optimum coherence
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.
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. 40971198 and 40701106)
East China Electronic Institute is acknowledged for provision of airborne SAR data
