Higher Order Statistics for Texture Analysis and Physical Interpretation of Polarimetric SAR Data

The logarithmic cumulants (log-cumulants for short) of the second and third orders are widely used in the statistical analysis of polarimetric synthetic aperture radar (PolSAR) data. However, both the product model and the finite mixture model may produce the same values of these statistics, which means that the use of these log-cumulants is not enough to determine the statistical model of the data. In this letter, it is demonstrated that the log-cumulants of higher orders can help to distinguish the concept of texture from that of mixture, providing a physical insight into the data statistics. A tool called log-cumulant cube, which helps to visualize this difference, is proposed by considering texture distributions from the Pearson's family. Results on both simulated and real SAR data show that the use of higher order statistics is useful when it comes to the texture analysis of PolSAR data.