Hyperspectral Target Detection: Hypothesis Testing, Signal-to-Noise Ratio, and Spectral Angle Theories

Hyperspectral target detection (HTD) can be generally categorized by its targets to be detected, $a$ priori targets with provided known target knowledge as $a$ priori target detection and $a$ posteriori targets with known target signatures (spectral shapes), but unknown abundance fractions needed to be estimated as $a$ posteriori target detection. As a result, target detection can be performed in three scenarios, full pure-pixel target detection corresponding to $a$ priori target detection, and subpixel and mixed-pixel target detection corresponding to $a$ posteriori target detection. To develop theories for these three types of target detection, this article develops three approaches. One is to rederive hypothesis testing-based detection theory using very basic statistical detection theory. Another two are new theories, signal-to-noise ratio (SNR)-based detection theory that uses SNR as a criterion to derive optimal detectors and spectral angle (SA)-based detection theory that calculates SA to perform HTD, both of which do not require prior probability distributions as hypothesis testing does. Specifically, it will be shown that many current hypothesis testing-derived likelihood ratio test (LRT)-based detectors can find their counterparts in the SNR-derived theory and the SA-derived detection theory. Finally, to evaluate the detection performance among the detectors developed from these three approaches, several effective detection measures resulting from 3-D receiver operating characteristic (ROC) analysis are used to conduct a comprehensive study and comparative analysis.