Anomaly detection using spectral unmixing with negative and superunity abundance weights

We propose a low false alarm methodology to determine anomalies in hyperspectral data. The method is based on the assumption that due to the resolution of the image, most pixels are mixtures of pure substances, which are relatively rare in the scenes. In the first stage of the algorithm, the background classes, which are the dominant classes in the image, are found. The method consists of robust clustering of a randomly-chosen small percentage of the image pixels. The resulting clusters may be considered as representatives of the background classes in the image. In order to determine the anomalous pixels, a threshold may be applied to the distance between the pixel spectrum and the cluster centres. However, pixels corresponding to anomalies and pure substances will both show high distances. If we consider that the background classes are themselves most likely mixtures of other materials, the pixels within the convex hull formed by the background classes will have positive fractions that are smaller than 1. The pure substances, however, will be outside such a convex hull, and will show negative or superunity fractions. We propose to use the unmixing spectral linear model without the non-negativity constraint, to distinguish between false anomalies corresponding to pure substances and real man-made anomalies.