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Sparse modeling is a powerful framework for data analysis and processing. It is especially useful for high-dimensional regression and classification problems in which a large number of feature variables exist but the amount of training samples is limited. In this paper, we address the problems of feature description, feature selection and classifier design for hyperspectral images using structured sparse models. A linear sparse logistic regression model is proposed to combine feature selection and pixel classification into a regularized optimization problem with the constraint of sparsity. To explore the structured features, three-dimensional discrete wavelet transform (3D-DWT) is employed, which processes the hyperspectral data cube as a whole tensor instead of adapting the data to a vector or matrix. This allows more effective capturing of the spatial and spectral structure. The structure of the 3D-DWT features is imposed on the sparse model by group LASSO which selects the features on the group level. The advantages of our method are validated on the real hyperspectral data.