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In this paper, a new technique for hyperspectral image classification is proposed. Our approach relies on the sparse representation of a test sample with respect to all training samples in a feature space induced by a kernel function. Projecting the samples into the feature space and kernelizing the sparse representation improves the separability of the data and thus yields higher classification accuracy compared to the more conventional linear sparsity-based classification algorithm. Moreover, the spatial coherence across neighboring pixels is also incorporated through a kernelized joint sparsity model, where all of the pixels within a small neighborhood are sparsely represented in the feature space by selecting a few common training samples. Two greedy algorithms are also provided in this paper to solve the kernel versions of the pixel-wise and jointly sparse recovery problems. Experimental results show that the proposed technique outperforms the linear sparsity-based classification technique and the classical Support Vector Machine classifiers.