Sparse Representation with Constraints for Target Detection in Hyperspectral Imagery

In this paper, we propose a constrained sparse representation (CSR) based algorithm for target detection in hyperspectral imagery. This algorithm is based on the concept that each pixel lies in a low-dimensional subspace spanned by target and background training samples. Therefore, it can be linearly represented by these samples weighted by a sparse vector. According to the spectral linear mixture model (LMM), the non-negativity constraint and sum-to-one constraint are imposed to the sparse vector. According to the Karush Kuhn Tucker (KKT) conditions, the upper bound constraint on sparsity level is removed. Besides, to alleviate the effects of target contamination in the background dictionary, an upper bound constraint is given to the weights corresponding to the atoms in the background dictionary. Finally, this constrained sparsity model is solved by a fast sequential minimal optimization (SMO) method. Different from other sparsity-based models, both the residuals and weights are used to detect targets in our algorithm, resulting in a better detection performance. The major advantage of the proposed method is the capability to suppress target signals in the background dictionary. The proposed method was compared to several traditional detectors including spectral matched filter (SMF), adaptive subspace detector (ASD), matched subspace detector (MSD), and sparse representation (SR) based detector. The commonly used receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are adopted for performance evaluation. Extensive experiments are conducted on two real hyperspectral data sets. It is demonstrated that our CSR method is robust to different target contamination levels in the background dictionary. From these experiments, it can be seen that our CSR method achieves a much higher target detection probability than other traditional methods at all false alarm rates. Meanwhile, our CSR method achieves the highest AUC value, which is significantly larger than most traditional methods. Moreover, the proposed method also have a relatively low computational cost.