Anomaly detection in noisy hyperspectral imagery

Anomaly detection in hyperspectral imagery seeks to identify a small subset of pixels whose spectra differ most significantly from the background. The challenge is to characterize the background and noise well enough to recognize which observations are truly distinct and not simply noise outliers. The covariance-based RXD operator was developed to select low-probability pixel spectra and is therefore sensitive to noise. We compare the RXD operator to a Euclidean metric weighted by the inverse of the estimated spectral noise variance. We then combine the weighted Euclidean metric with RXD using a Lagrange multiplier and demonstrate that this formulation retains RXD's emphasis on small clusters while controlling the impact of noise. An optimum value of the Lagrange multiplier is determined based on the number of bands. We explore the utility of normalizing the pixel spectra as a step in anomaly detection. Results for the RXD, weighted-Euclidean, and Lagrange approach are presented using AVIRIS and HYDICE imagery. Based on these results, we conclude that the Euclidean, although robust to noise, does little more than emphasize the brightest pixels. The Lagrange detector selects the same regions as RXD while significantly reducing the impact of noise.