A Constrained Sparse-Representation-Based Binary Hypothesis Model for Target Detection in Hyperspectral Imagery

In this paper, we propose a novel constrained sparse-representation-based binary hypothesis model for target detection in hyperspectral imagery. This model is based on the concept that a target pixel can only be linearly represented by the union dictionary combined by the background dictionary and target dictionary, while a background pixel can be linearly represented by both the background dictionary and the union dictionary. To be physically meaningful, the non-negativity constraint is imposed to the weight vector. To suppress the target signals in the background dictionary, the upper bound constraint is also imposed to the weight vector. These upper bounds are adaptively estimated by the similarities between the atoms in the background dictionary and target. Then, the weight vectors under different hypotheses are recovered by a fast coordinate descent method. Finally, both the residual difference and weight difference between the two hypotheses are used to perform the target detection. An important advantage of the proposed method is the robustness to varying target contamination. Extensive experiments conducted on real and synthetic hyperspectral datasets have demonstrated the superiority of the proposed detector in detection performance and computational cost. Specifically, for the Avon dataset, our method achieves the highest area under the receiver operating characteristic (ROC) curve of 99.91%, and achieves the shortest runtime of 109.76 s.