A Linearly Constrained Signal Subspace Projection Approach Developed to Detect Targets in Hyperspectral Images

Hyperspectral images have been widely used for target detection. In general, target signatures should be known a priori for filter-based detection methods. However, the uncertainty of target signatures caused by the influence of atmospheric interference or other random noise degrades the detection performance. Therefore, developing a robust detection method is crucial in hyperspectral image analysis. In this study, a linearly constrained signal subspace projection approach for target detection is proposed. Instead of using a single constraint on target detection, an optimal filter with multiple constraints is designed using signal subspace projection (SSP). The SSP approach fully exploits the orthogonal property of two orthogonal subspaces; one denotes a signal subspace that contains desired targets and undesired interference, and the other denotes a noise subspace, which is orthogonal to signal subspace. By projecting the weights of the detection filter on the signal subspace, the proposed SSP reduces estimation errors in target signatures and alleviates the performance degradation caused by the uncertainty of target signatures. The SSP approach can detect desired targets, suppress undesired targets, and minimize interference effects. In this paper, three methods are provided for selecting multiple constraints of the desired target: K-means, principal eigenvectors, and endmember extraction techniques. The simulation results show that the proposed SSP with multiple constraints on the desired target selected using K-means has superior detection performance. Further-more, the proposed SSP with multiple constraints is less sensitive to the uncertainty of target signatures.