  Dictionary learning algorithms have been successfully used in both
reconstructive and discriminative tasks, where the input signal is represented
by a linear combination of a few dictionary atoms. While these methods are
usually developed under $\ell_1$ sparsity constrain (prior) in the input
domain, recent studies have demonstrated the advantages of sparse
representation using structured sparsity priors in the kernel domain. In this
paper, we propose a supervised dictionary learning algorithm in the kernel
domain for hyperspectral image classification. In the proposed formulation, the
dictionary and classifier are obtained jointly for optimal classification
performance. The supervised formulation is task-driven and provides learned
features from the hyperspectral data that are well suited for the
classification task. Moreover, the proposed algorithm uses a joint
($\ell_{12}$) sparsity prior to enforce collaboration among the neighboring
pixels. The simulation results illustrate the efficiency of the proposed
dictionary learning algorithm.
