Evaluating and improving local hyperspectral anomaly detectors

This paper addresses two issues related to the detection of hyperspectral anomalies. The first issue is the evaluation of anomaly detector performance even when labeled data is not available. The second issue is the estimation of the covariance structure of the data in local detection methods, such as the RX detector, when the number of available training pixels n is not much larger than (and may even be smaller than) the data dimensionality p. Our first contribution is to formulate and employ a mean-log-volume approach for evaluating local anomaly detectors. Traditionally, the evaluation of a detector´s accuracy has been problematic. Anomalies are loosely defined as pixels that are unusual with respect to the other pixels in a local or global context. This loose definition makes it easy to develop anomaly detection algorithms and many have been proposed but more difficult to evaluate or compare them. Our mean-log-volume approach allows for an effective evaluation of a detector´s accuracy without requiring labeled testing data or an overly-specific definition of an anomaly. The second contribution is to investigate the use of the Sparse Matrix Transform (SMT) to model the local covariance structure of hyperspectral images. The SMT has been previously shown to provide full rank estimates of large covariance matrices even in the n <; p scenario. Traditionally, the number of training pixels needed for good estimates of the covariance needs to be at least as large as the data dimensionality (and preferably it should be several times larger). Therefore, when one deploys the RX detector in a sliding window, the choices to select small window sizes are limited because of the n >; p restriction associated to the covariance estimation. Our results suggest that RX-style detectors using the SMT covariance estimates perform favorably compared to other methods even (indeed, especially) in the regime of very small window sizes.