Alternative Asymmetric Hypothesis Tests for Hyperspectral Imagery; Final rept

摘要

This report focuses on the development of statistical anomaly detection techniques aimed at accentuating the presence of meaningful objects, e.g., a land vehicle, as a collection of localized anomalies in reference to a scene dominated by natural clutter backgrounds. The report presents a significant improvement in anomaly detection performance via a principle of indirect comparison, where samples are not compared to each other as individual entities, but as individual entities compared to the union of these entities. Let X and Y denote two random samples, and let Z = X U Y, where U denotes the union. X can be indirectly compared to Y by comparing instead some of the corresponding distribution attributes of Z and Y. This idea led to the development of four unconventional techniques for hyperspectral (HS) anomaly detection. The first technique is based on some of the advances made on semiparametric (large sample) inference, where a logistic model and its maximum likelihood method are presented, along with the analysis of its asymptotic behavior. The second technique is based on fundamental theorems from large sample theory and is developed to approximate performance of the former technique, albeit free from its implementation drawbacks. A third detector is developed, as an alternative, using the same principle and a known property of the F-distribution family. The introduction of this third detector, which has an asymptotic F-distribution behavior, was motivated by the classic one-way ANOVA, which under its null hypothesis and the normality assumption has a test statistic governed by an exact F distribution. Finally, a fourth and significantly more compact technique is developed based on an asymmetric variance test between the union of two samples and one of the individual samples. Like the previous three techniques, this compact form is free from distribution assumptions, although under its null hypothesis the test statistic converges to a known distribution.