Abstract
In this paper, we investigate the anomaly detection problem for widespread targets with known spacial patterns under a local Gaussian model when training data are available. Three adaptive detectors are proposed based on the principles of the generalized likelihood ratio test, the Rao test, and the Wald test, respectively. We prove that these tests are statistically equivalent to each other. In addition, analytical expressions for the probability of false alarm and probability of detection of the proposed detectors are obtained, which are verified through Monte Carlo simulations. It is shown that these detectors have a constant false alarm rate against the covariance matrix. Finally, numerical examples using synthetic and real hyperspectral data demonstrate that these training data assisted detectors have better detection performance than their counterparts without training data.
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