Sparsity-based classification of hyperspectral imagery

In this paper, a new sparsity-based classification algorithm for hyperspectral imagery is proposed. This algorithm is based on the concept that a pixel in hyperspectral imagery lies in a low-dimensional subspace and thus can be represented by a sparse linear combination of the training samples. The sparse representation (a sparse vector representing the selected training samples) of a test sample can be recovered by solving a constrained optimization problem. Once the sparse vector is obtained, the class of the test sample can be directly determined by the behavior of the vector on reconstruction. In addition to the constraints on sparsity and reconstruction accuracy, we also exploit the fact that hyperspectral images are usually smooth within a neighborhood. In our proposed algorithm, a smoothness constraint is imposed by forcing the Laplacian of the reconstructed image to be minimum in the optimization process. The proposed sparsity-based algorithm is applied to several hyperspectral imagery to classify the pixels into target and background classes. Simulation results show that our algorithm outperforms the classical hyperspectral target detection algorithms, such as the popular spectral matched filters, matched subspace detectors, and adaptive subspace detectors.