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This paper investigates the joint-structured-sparsity-based methods for transient acoustic signal classification with multiple measurements. By joint structured sparsity, we not only use the sparsity prior for each measurement but we also exploit the structural information across the sparse representation vectors of multiple measurements. Several different sparse prior models are investigated in this paper to exploit the correlations among the multiple measurements with the notion of the joint structured sparsity for improving the classification accuracy. Specifically, we propose models with the joint structured sparsity under different assumptions: same sparse code model, common sparse pattern model, and a newly proposed joint dynamic sparse model. For the joint dynamic sparse model, we also develop an efficient greedy algorithm to solve it. Extensive experiments are carried out on real acoustic data sets, and the results are compared with the conventional discriminative classifiers in order to verify the effectiveness of the proposed method.