12.1 Introduction

Multidimensionality arises in SAR data whenever the same scene is imaged in several channels, which may be separated by differences in polarization, frequency, time, aspect angle, or incidence angle. All of these can be exploited to provide extra information. A fundamental distinction between multidimensional data types is whether the channels are correlated at the pixel level or not. When correlation is present, the correlation parameters provide possible extra information about the scene. However, as we shall see, correlation can reduce our ability to remove speckle by combining channels. Images gathered in nonoverlapping frequency bands are expected to be uncorrelated. Multitemporal images of many types of terrain are correlated over short time scales (and hence can be exploited for interferometry) but decorrelate if the images are gathered a long time apart. The decorrelation time is highly dependent on the frequency and the terrain type (essentially because it depends on significant changes in the relative positions of the scatterers contributing to the return at a particular frequency). Interchannel correlation is an essential feature of polarimetric SAR but, as noted in Chapter 11, is nonzero only for the copolarized channels when the target displays azimuthal symmetry.

In this chapter, we discuss a variety of ways to extract the information present in multidimensional data. Here another important distinction is needed between the statistical information available from a distributed target and the structural information that defines the shapes and boundaries that mark out those distributed targets. In the first case...