Coincidence of the Rao Test, Wald Test and GLRT for anomaly detection in hyperspectral imagery

摘要

Anomaly detection methods are designed to detect targets (small anomalies) without a priori information on the target spectral signature. In this letter, we deal with the problem of anomaly detection for hyperspectral images based on the Gaussian model assuming that the background obeys a real-valued Gaussian multivariate distribution with unknown covariance matrix. This model is widely used in hyperspectral images. We derive the corresponding Rao and Wald tests, and show that both the two tests are equivalent to the generalized likelihood ratio test.