Hyperspectral Anomaly Detection by Data Sphering and Sparsity Density Peaks

Many approaches have been developed for hyperspectral anomaly detection (AD). Of particular interest are low rank and sparse representation (LRaSR) model-based methods which decompose a data space into low rank and sparse spaces. This article develops a rather different approach, which assumes that background (BKG) and anomalies can be, respectively, characterized by data statistics of the first two orders (2OS) and high orders (HOS) greater than 2. As a result, data sphering (DS) can remove BKG, while the fast independent component analysis (FastICA) can generate independent components (ICs) to form a sparse space. However, since non-Gaussian noises cannot be separated by FastICA, directly extracting anomalies from the ICs-formed sparse space may not be effective. To address this issue, a new concept of sparsity density peak (SDP) is proposed to represent the data samples in the sparse space as a probability density function from which a set of data samples with peaks can be extracted to form an anomaly space. Three versions of SDP, fixed spectral SDP (FS-SDP), fixed band SDP (FB-SDP), and spectral–spatial–sparsity peak (SS-SDP) are derived and used where the number of peaks to be extracted is determined by virtual dimensionality (VD) and a minimax-singular value decomposition (MX-SVD) algorithm. The experimental results demonstrate that DS coupled with SDP performs better than currently being used LRaSR model-based methods in AD.