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 hzhang@ceode.ac.cn Vancouver, Canada July 29, 2011

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

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.

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.

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

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

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

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:

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

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

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

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

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

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