Hyperspectral Data Processing: Algorithm Design and Analysis

2.2 Subsample Analysis

The most fundamental task in subsample analysis is subsample detection where two types of detectors will be discussed in this section, detectors with hard decisions and detectors with soft decisions, which correspond to pure-sample target detector and subsample target detector, respectively.

2.2.1 Pure-Sample Target Detection

Despite that a subsample target may be present in a sample, the pure-sample target detection is performed by forcing a detector to make a binary decision, whether the sample is to be detected as target sample or not. In other words, the pure-sample target detection can only say “yes” if target is detected and “no” if target is absent. So, even though a subsample target does not fully occupy the entire sample, it must be claimed to be a pure target sample if a detector says “yes” as target is detected. To emphasize such a nature, the commonly used binary hypotheses-based detectors described in the following are called pure-sample target detectors.

A classical approach to pure-sample target detection is to formulate a signal detection problem as the following binary hypothesis-testing problem.

(2.1)

where r is an observable random variable; the null hypothesis H₀ and alternative hypothesis H₁ represent the case of target absence and the case of target presence with their probability distributions specified by P₀(r) and P₁(r), respectively. ...