A Constrained Sparse Representation Model for Hyperspectral Anomaly Detection

In this paper, we propose a novel sparsity-based algorithm for anomaly detection in hyperspectral imagery. The algorithm is based on the concept that a background pixel can be approximately represented as a sparse linear combination of its spatial neighbors while an anomaly pixel cannot if the anomalies are removed from its neighborhood. To be physically meaningful, the sum-to-one and nonnegativity constraints are imposed to abundance vector based on the linear mixture model, and the upper bound constraint on sparsity level is removed for better recovery of the test pixel. First, the proposed method utilizes the redundant background information to automatically remove anomalies from the background dictionary. Then, the reconstruction error obtained by the new background dictionary is directly used for anomaly detection. Moreover, a kernel version of the proposed method is also derived to completely exploit the nonlinear feature of hyperspectral data. An important advantage of the proposed methods is their capability to adaptively model the background even when some anomaly pixels are involved. Extensive experiments have been conducted on three real hyperspectral data sets. It is demonstrated that the proposed detectors achieve a promising detection performance with a relatively low computational cost.