Anomaly detection with sparse unmixing and gaussian mixture modeling of hyperspectral images

One of the main applications of hyperspectral image analysis is anomaly detection where the problem of interest is the detection of small rare objects that stand out from their surroundings. A common approach to anomaly detection is to rst model the background scene and then to use a detector that quanti es the di erence of a particular pixel from this background. However, identifying the dominant background components and modeling them is a challenging task. We propose an anomaly detection framework that uses Gaussian mixture models for characterizing the scene background in hyperspectral images. First, the full spectrum is divided into several contiguous band groups for dimensionality reduction as well as for exploiting the peculiarities of di erent parts of the spectrum. Then, sparse spectral unmixing is performed for each band group for identifying signi cant endmembers in the scene. Three methods for identifying the dominant background groups such as thresholding, hierarchical clustering and biclustering are used in the endmember abundance space to retrieve the sets of pixel groups that represent dominant background components. Next, these pixel groups are used for initializing individual Gaussian mixture models that are estimated separately for each spectral band group. The proposed method enables automatic identi cation of the number of mixture components and e ective initialization of the estimation procedure for the mixture model. Finally, the Gaussian mixture models for all groups are statistically fused for obtaining the nal anomaly map for the scene. Comparative experiments showed that the proposed methods performed better than two other density-based anomaly detectors, especially for small false positive rates, on an airborne hyperspectral data set.