Analysis of spectral mixtures is important in remote sensing imaging spectroscopy, because essentially the spectrum of any pixel of a natural scene is a mixture. The analysis of mixed spectra, known as Spectral Mixture Analysis (SMA), is the subject of this chapter. SMA attempts to answer two questions: (a) What are the spectra of the individual materials? (b) What are the proportions of the individual materials? We focus on linear mixing because of its relative analytical and computational simplicity and because it works satisfactorily in many practical applications.We discuss the physical aspects of the linear mixing model, geometrical interpretations and algorithms, and statistical analysis using the theory of least squares estimation. The main applications of SMA are in the areas of hyperspectral image interpretation and subpixel target detection.

Spectral Mixing

When a ground resolution element contains several materials, all these materials contribute to the individual pixel spectrum measured by the sensor. The result is a composite or mixed spectrum, and the “pure” spectra that contribute to the mixture are called endmember spectra. Spectral mixtures can be macroscopic or intimate depending on what scale the mixing is taking place (see Figure 9.1).

In a macroscopic mixture the materials in the field of view are optically separated in patches so there is no multiple scattering between components (each reflected photon interacts with only one surface material). Such mixtures are linear: that is, the combined spectrum is simply the sum of the fractional area times the spectrum of each component. Linear mixing is possible as long as the radiation from component patches remains separate until it reaches the sensor.

In an intimate mixture, such as the microscopic mixture of mineral grains in a soil or rock, a single photon interacts with more than one material. In this case, mixing occurs when radiation from several surfaces combines before it reaches the sensor. These types of mixtures are nonlinear in nature and therefore more difficult to analyze and use.

To illustrate some of the issues involved in SMA, we discuss some examples of mixed spectra provided by Adams and Gillespie (2006). Figure 9.2(a) shows spectra for mixtures of a material having a featureless spectrum (quartz) with a material having a spectrum with diagnostic absorption bands (alunite).