Statistical Tests for Symmetries in Polarimetric Scattering Coherency Matrices

The second-order statistics are among the most important observables in synthetic aperture radar (SAR) polarimetry and are usually reported as covariance or coherence matrices. They are restricted to particular forms provided the target exhibits a certain kind of symmetry. As these constraints are not exactly fulfilled in real data, statistical tests are proposed for checking the validity of an invariance hypothesis. The application of these likelihood-ratio tests to airborne L-band data reveals a strong dependence of the test statistics on both the land cover and the number of looks; furthermore, temporal changes such as vegetation growth are evident: for example, lack of reflection symmetry for mature rape fields. This finding is at odds with commonly employed models, which assume (and predict) reflection invariance. For the Freeman-Durden decomposition, which relies on reflection symmetry, the connection between this invariance and negative powers (unphysical result) is found to be weak.

[1]  Ramesh A. Gopinath,et al.  Maximum likelihood modeling with Gaussian distributions for classification , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[2]  Shane Cloude,et al.  The structure of oriented vegetation from polarimetric interferometry , 1999, IEEE Trans. Geosci. Remote. Sens..

[3]  M. Moghaddam Effect of Medium Symmetries On Parameter Estimation With Polarimetric Interferometry , 2000 .

[4]  C. Gouriéroux,et al.  Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters , 1982 .

[5]  S. Cloude Polarisation: Applications in Remote Sensing , 2009 .

[6]  Hiroyoshi Yamada,et al.  Four-Component Scattering Power Decomposition With Rotation of Coherency Matrix , 2011, IEEE Trans. Geosci. Remote. Sens..

[7]  Adrian K. Fung,et al.  Backscattering from a randomly rough dielectric surface , 1992, IEEE Trans. Geosci. Remote. Sens..

[8]  Laurent Ferro-Famil,et al.  Analysis of Natural Scenes using Polarimetric and Interferometric SAR Data Statistics in Particular Configurations , 2008, IGARSS 2008 - 2008 IEEE International Geoscience and Remote Sensing Symposium.

[9]  R. Kwok,et al.  Polarimetric scattering and emission properties of targets with reflection symmetry , 1994 .

[10]  Irena Hajnsek,et al.  Inversion of surface parameters from polarimetric SAR , 2003, IEEE Trans. Geosci. Remote. Sens..

[11]  Stephen L. Durden,et al.  A three-component scattering model for polarimetric SAR data , 1998, IEEE Trans. Geosci. Remote. Sens..

[12]  Eric Pottier,et al.  A review of target decomposition theorems in radar polarimetry , 1996, IEEE Trans. Geosci. Remote. Sens..

[13]  I. Campbell Chi‐squared and Fisher–Irwin tests of two‐by‐two tables with small sample recommendations , 2007, Statistics in medicine.