Modeling magnitude statistics of multilook SAR interferograms by generalizing G distributions

Statistical analysis of multilook interferograms is a foundational issue in sensor signal processing of multiple-channel synthetic aperture radar (SAR), such as slow ground moving target indication (GMTI) in along-track interferometric (ATI) SAR. By an approximate derivation of the product of two modified Bessel functions, we propose in this paper a distribution (denoted simply as ΓIn) to model the interferometric magnitude of homogeneous clutter and analyze the capability of approximation using ΓIn according to numerical calculations. Following this, under the frame of the product model and by utilizing ΓIn, we analytically provide two distributions, KIn and GIn0, corresponding to heterogeneous and extremely heterogeneous terrain clutter, respectively. We show that the proposed ΓIn,KIn and GIn0 are the multi-channel generalizations of the well-known Γ,K and G0, respectively, which belong to the special cases of G distribution for single-channel SAR images. Finally, the estimators of the proposed models are obtained by applying the Method of Log Cumulants (MoLC), which can accurately calculate the contained parameters. Experiments performed on the National Aeronautics and Space Administration Jet Propulsion Laboratory's (NASA/JPL) AirSAR images that used the Kullback-Leibler (KL) divergence as a similarity measurement verified the performance of the proposed models and estimators.