Polarimetric SAR Modelling: Mellin Kind Statistics and Time-Frequency Analysis

Polarimetric synthetic aperture radar (PolSAR) remote sensing refers to measurement techniques that exploit the ability of a back scattering target to transform the polarization state of incoming electromagnetic waves to extract information. This field of remote sensing deals with complex, multi-dimensional data sets, requiring multi-dimensional signal analysis strategies. Target information is in general extracted from PolSAR data by an analysis approach referred to as polarimetric target decompositions, a field of research which has been successfully developed over the last few decades. Low resolution SAR images of distributed natural scenes contain a high number of scatterers within each resolution cell, resulting in Gaussian signal statistics. Gaussian signal statistics and target decompositions found the basis for classical analysis of PolSAR data. With the improving spatial resolution of currently operating SARs, the Gaussian assumption is frequently challenged and often abandoned, in particular for scenes of urban environment, but also for natural surfaces such as forest and sea. This development has stimulated research on non-Gaussian models for representing the statistics of SAR and PolSAR signals. In particular, non-Gaussian modelling of multi-dimensional SAR signals using the doubly stochastic product model has received an increased attention in recent years. The chapter will give a brief introduction to techniques for analysis of PolSAR data using statistical signal processing. Here two axes will be explored: one that focuses on non-Gaussian signals statistics, including sections on modelling, estimation, and classification; and one that focuses on the signals time-frequency properties, discussing target detection and discrimination.