Peifeng Ma FR01 T01 5.ppt

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

hzhang@ceode.ac.cn

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