Local Sparsity Divergence for Hyperspectral Anomaly Detection

Anomaly detection (AD) has increasingly become important in hyperspectral imagery (HSI) owing to its high spatial and spectral resolutions. Many anomaly detectors have been proposed, and most of them are based on a Reed-Xiaoli (RX) detector, which assumes that the spectrum signature of HSI pixels can be modeled with Gaussian distributions. However, recent studies show that the Gaussian and other unimodal distributions are not a good fit to the data and often lead to many false alarms. This letter proposes a novel hyperspectral AD algorithm based on local sparsity divergence (LSD) without any distribution hypothesis. Our algorithm exploits the fact that targets and background lie in different low-dimensional subspaces and that targets cannot be effectively represented by their local surrounding background. A sliding dual-window strategy is first adopted to construct local spectral and spatial dictionaries, which enable the extraction of the sparse coefficients of each HSI pixel. Then, a consistent sparsity divergence index is proposed to compute the LSD map at each spectral band separately. Finally, joint segmentation of LSD maps over different bands is performed for AD. Experimental results on both simulated data and recorded data demonstrate the effectiveness of the proposed algorithm.