Dual versus Quadpol: A New Test Statistic for Radar Polarimetry
(1) AEL Consultants, 26 Westfield Avenue, KY15 5AA Cupar, United Kingdom
There is currently much discussion about the relative trade-offs between dual and compact polarization modes versus full quad-polarimetry in future SAR sensors. The former offer advantages of swath coverage and data rate reduction whereas the latter offers maximum flexibility in the utilization of polarization information for remote sensing applications. However, while this extra flexibility is proven useful in urban and agricultural areas, there remains an important question as to the need for full quadpol data in complex random scattering media such as forestry. Such media form an important class of remote sensing applications, with for example global forest biomass and stem volume being desired products for input to global climate models. This is further complicated by dependence on sensor parameters such as wavelength, resolution, incidence angle etc.
In this paper we devise a new test statistic, applicable to all quadpol data sets, and designed to show clearly those regions where quadpol data is and is not required. Such tests have been proposed already in the literature  but they suffer from two important drawbacks, the first is their lack of physical interpretation in terms of scattering mechanisms and the second their difficulty in dealing with singular coherency matrices, as occur often, especially in low frequency (P and L band) SAR imagery.
We overcome these two limitations by basing our test on the entropy/alpha decomposition , which gives a clear physical interpretation and secondly allows treatment of scatterers with zero entropy (singular matrices) as well as high entropy volume scatterers.
The test is based on three key ideas. The first being that for random scattering media where a two parameter dual polarization description is adequate, their H/α response lies along the lower bound of the entropy/alpha diagram (azimuthal symmetry line). We then use this to compare the observed alpha value for the pixel against a prediction based on the assumption of azimuthal symmetry. In the second stage we show that for Wishart statistics this difference has a Rayleigh distribution with an entropy dependent width parameter. We can then use this in the third and final stage to design an adaptive test statistic to determine the probability that an observed pixel contains dual or quad polarization information.
We first describe the algorithm in detail and then apply it to ALOS-PALSAR data for different forest environments to illustrate its utility and robustness in different applications.
 Ferro-Famil L., M Neumann, “Recent Advances in the Derivation of POLInSAR Statistics: Study and Applications”, Proceedings of 7th European Conference on Synthetic Aperture Radar (EUSAR), Friedrichshafen, Germany, Vol. 2, pp143-146, June 2008
 Cloude S.R., E. Pottier, "An Entropy Based Classification Scheme for Land Applications of Polarimetric SAR", IEEE Transactions on Geoscience and Remote Sensing, Vol. 35, No. 1, pp 68-78, January 1997