Local density based potential dictionary construction for low rank representation in hyperspectral anomaly detection

Anomaly detection plays a significant role in hyperspectral imagery. Traditional methods mainly focus on the spectral discrimination between the background object and the test object by means of utilizing the Mahalanobis distance such as the benchmark Reed-Xiaoli (RX) detector. In this paper, we propose a novel hyperspectral anomaly detection method based on low rank representation. Since the observed hyperspectral data can be decomposed into a background part with low-rank property and a sparse anomaly part, we exploit the local outlier factor (LOF) to construct the potential background dictionary. The dictionary attempts to cover as many categories as possible for the potential background objects and can effectively excludes the anomaly objects by calculating the local density and outlier degree. In order to take advantage of the huge hyperspectral dataset cube, we integrate the spectral and spatial information with the outlier degree as a constraint component to optimize the low rank representation model, which takes the implicit structure of the whole hyperspectral image into consideration. Experiments conducted on both synthetic and real hyperspectral datasets indicate the proposed method achieves a better performance compared to other state-of-the-art methods.