Kernel Sparse Representation for Hyperspectral Target Detection

A nonlinear kernel-based classifier for hyperspectral target detection is proposed in this paper. The proposed approach relies on sparsely representing a test sample in terms of all the training samples in a high-dimensional feature space induced by a kernel function. Specifically, the feature representation of a test pixel is assumed to be compactly expressed as a sparse linear combination of few atoms from a training dictionary consisting of both background and target training samples in the same feature space. The sparse representation vector is obtained by decomposing the test pixel over the training dictionary via a kernelized greedy algorithm, which uses the kernel trick to avoid explicit evaluations of the data in the feature space. The class label is then determined by comparing the reconstruction accuracy with respect to the background and target sub-dictionaries using the recovered sparse vector. Designing the classifier in a high-dimensional feature subspace will implicitly exploit the higher-order structure (correlations) within the data which cannot be captured by a linear model. Therefore, by projecting the pixels into a kernel feature space and kernelizing the linear sparse representation model, the data separability between the background and target classes will be shown to be improved, leading to a more accurate detection performance. The effectiveness of the proposed kernel sparsity model for target detection is demonstrated by experimental results on real hyperspectral images.