In the previous chapter, we considered how we might best detect small, localised targets in a background of sea clutter. The identification of the likelihood ratio as an optimum discriminant, and of its more practically useful approximations, provided us with a unifying framework for this discussion. However, small target returns are not the only features of interest in maritime radar imagery. Large-scale correlated structures arising from surface currents, ship wakes, the presence of surfactants and other sources can frequently be discerned and are a valuable source of information in many circumstances. In this chapter, we will discuss how such ocean surface features might best be enhanced and detected. Once again the likelihood ratio concept is a very useful guiding principle, which leads us to methods that enable us to both enhance these features and exploit our prior knowledge of their structure to detect them more effectively. So, paradoxically, a discussion of the processing of images, which are frequently interpreted and assessed in qualitative terms, will involve us in a fair amount of detailed formal analysis. Much of this will be based on the multivariate Gaussian distribution; we commence this chapter with a review of its pertinent properties, which are discussed in more detail in Chapter 5.

Chapter Contents:

• 11.1 Introduction
• 11.2 The analysis of correlated Gaussian data
• 11.2.1 χ processing
• 11.2.2 χa processing and the whitening filter
• 11.2.3 Optimal χo processing
• 11.3 The Wishart distribution
• 11.3.1 The real Wishart distribution
• 11.3.2 The complex Wishart distribution
• 11.4 Polarimetric and interferometric processing
• 11.4.1 χ processing of interferometric and polarimetric data
• 11.4.2 Phase increment processing of interferometric data
• 11.4.3 Coherent summation and discrimination enhancement
• 11.5 Feature detection by matched filtering
• 11.6 False alarm rates for matched filter processing
• 11.6.1 A simple model for the global maximum single point statistics
• 11.6.2 The global maximum of a one-dimensional Gaussian process and the matched filter false alarm curve for a time series
• 11.6.3 Extension to two-dimensional matched filters
• 11.7 A compound model for correlated signals
• References

Inspec keywords: Gaussian distribution; radar clutter; oceanographic techniques; radar imaging; marine radar; maximum likelihood estimation

Other keywords: sea clutter; multivariate Gaussian distribution; maritime radar imagery; ocean surface feature; likelihood ratio

Subjects: Optical, image and video signal processing; Radar equipment, systems and applications; Oceanographic and hydrological techniques and equipment; Other topics in statistics