11.10 Interferometric, Multifrequency, and Multitemporal Data

Although the developments in this chapter have been principally motivated by the properties of polarimetric data, they are applicable to other forms of multidimensional data, with some simplifications and modifications. Closest in spirit to polarimetric data is interferometric data, since this is critically dependent on correlation between channels, where now the channels are distinguished by their viewing angle of the scene [47]. In fact, all the information characteristic of interferometry is carried by the complex correlation of channels, from which can be inferred, inter alia, a terrain map of the scene [48, 49], disturbances to the surface due to agricultural treatment [50], and surface motion or deformation [51]. Hence, from the point of view of image statistics, interferometric data have the same properties as polarimetric data because the channels will be jointly Gaussian (possibly with texture) and the quantities of interest are the complex correlation coefficients. The MLEs of interferometric phase and coherence are as described in Section 11.7. As noted there, accurate estimates of phase require high coherence or large numbers of samples. This has a direct impact on the properties of the information that can be extracted from interferometry. For example, accurate measurements of phase in areas of low coherence require a lot of spatial averaging, with consequent loss of spatial resolution. Since phase is the quantity used to infer topography, this affects the quality of any inferred digital elevation model; consistent height accuracy across a scene implies differing spatial resolution. Although...