CHAPTER 3
ADVANCED POLARIMETRIC CONCEPTS
Since the introduction of polarimetric radar data in the 1980s, many different analysis techniques have been investigated. Many of these are application specific. In this chapter we shall discuss the theoretical background for many of these techniques and compare the information that is provided by the different approaches. As we shall see, many of these techniques provide very similar information, with the result that the choice of analysis technique becomes more one of personal preference.
3.1 VECTOR-MATRIX DUALITY OF SCATTERER REPRESENTATION
In the previous chapter we demonstrated that the received power can be written in terms of the scatterer covariance matrix, as follows:
The superscript * denotes complex conjugation, and 
denotes the transpose operation. The vector T contains the same information as the original scattering matrix.
If we restrict ourselves to the backscatter direction where Shv = Svh, the usual forms for the antenna and scatterer vectors are
and
The covariance matrix as defined in this expression is a positive ...
