Sphericity of complex stochastic models in multivariate SAR images

Polarimetry and multi-pass interferometry extend the dimensionality of SAR images, therefore the necessity to have multivariate statistic (and non-Gaussian) distributions as models for these types of data: such are the SIRV (Spherically Invariant Random Vectors). However, as the stochastic model becomes more complex, correctly estimating its parameters gets difficult. More, although they are versatile, the SIRV models are not guaranteed to match the PolSAR / InSAR data. To evaluate the pertinence of those models with respect to the PolSAR and multi-pass InSAR data, through one of their most important statistic properties, namely sphericity, it is the purpose of this paper. The proposed analysis is illustrated with spaceborne multi-pass InSAR TerraSAR-X data.