A Randomized Subspace Learning Based Anomaly Detector for Hyperspectral Imagery

This paper proposes a randomized subspace learning based anomaly detector (RSLAD) for hyperspectral imagery (HSI). Improved from robust principal component analysis, the RSLAD assumes that the background matrix is low-rank, and the anomaly matrix is sparse with a small portion of nonzero columns (i.e., column-wise). It also assumes the anomalies do not lie in the column subspace of the background and aims to find a randomized subspace of the background to detect the anomalies. First, random techniques including random sampling and random Hadamard projections are implemented to construct a coarse randomized columns subspace of the background with reduced computational cost. Second, anomaly columns are searched and removed from the coarse randomized column subspace by solving a series of least squares problems, resulting in a purified randomized column subspace. Third, the nonzero columns in the anomaly matrix are located by projecting all the pixels on the orthogonal subspace of the purified subspace, and the anomalies are finally detected based on the L-2 norm of the columns in the anomaly matrix. The detection performance of RSLAD is compared with four state-of-the-art methods, including global Reed-Xiaoli (GRX), local RX (LRX), collaborative-representation based detector (CRD), and low-rank and sparse matrix decomposition base anomaly detector (LRaSMD). Experimental results show good detection performance of RSLAD with lower computational cost. Therefore, the proposed RSLAD offers an alternative option for hyperspectral anomaly detection.