The objective of hyperspectral target detection is to find objects of interest within a hyperspectral image by using the particular spectral features associated with an object's surface-material content. In some cases, the objects of interest make up a significant enough portion of the image to be treated as a material class, and the classification methods described in the previous chapter can be well suited for identifying them. In other cases, the objects of interest are more scarcely populated in the scene, and the problem of detection requires a different method of treatment. Typically, this involves hypothesis testing, where one of two decisions is made for each image spectrum: (1) the spectrum corresponds to the object of interest, called a target, or (2) it corresponds to something other than the target, referred to as background clutter.
This chapter describes many of the basic methods applied to the problems associated with hyperspectral target detection. As this problem has very strong parallels in fields such as communications, radar signal processing, and speech recognition, methods are generally drawn from the broader field of statistical signal processing and then adapted to the nature of hyperspectral imagery. The chapter begins with a brief review of target detection theory and then introduces various methods within a taxonomy centered on the use of a generalized likelihood ratio test for target detection.
14.1 Target Detection Theory
The target detection problem is known in statistical signal processing references as a hypothesis test between a null hypothesis H0 that asserts that the spectrum under test is associated with background clutter, and an alternative hypothesis H1 that asserts that the spectrum under test is a target (Scharf, 1991). Under the null hypothesis, spectrum x is an element of acceptance region A of a multidimensional data space, while under the alternative hypothesis, it is an element of rejection region R, meaning that the null hypothesis is rejected. One can identify an indicator function φ(x) that defines the detector according to