11.1 Introduction

Up to this point, we have been concerned only with the information carried by a single SAR image. Of increasing importance are SAR systems that provide multidimensional information via multiple frequencies or polarizations. Such systems provide a much enhanced capacity for investigating Earth terrain because different frequencies and polarizations allow the probing of different scattering mechanisms and different components of the scattering layers. For example, in forest imaging, modeling suggests that for shorter wavelengths the backscatter from mature conifers is dominated by direct crown backscattering at all polarizations but that at long wavelengths the main component of the return depends on the polarization: trunk-ground interactions dominate at HH, for VV the major contribution to the return is direct crown backscatter, while the HV return is predominantly due to the primary branches in the crown layer [1, 2].

As for single-channel data, a primary step in extracting information from such images is to develop a model of the image statistics for distributed scatterers because in many applications, such as agriculture, forestry, and hydrology, such targets are the objects of interest. Even when we are concerned with small scatterers, their detection and classification is crucially affected by their clutter surroundings. Hence, the main goal of this chapter is to establish statistical models appropriate to multichannel data, especially polarimetric data. We will find that much of the structure already developed in earlier parts of this book transfers naturally into higher dimensions and provides a clear guide as to what is meant...