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Hyperspectral images exhibit significant spectral correlation, whose exploitation is crucial for compression. In this paper, an efficient method for hyperspectral image compression is presented using the three-dimensional discrete cosine transform (3D-DCT) and support vector machine (SVM). The core idea behind our proposed technique is to apply SVM on the 3D-DCT coefficients of hyperspectral images in order to determine which coefficients (support vectors) are more critical for being preserved. Our method not only exploits redundancies between the bands, but also uses spatial correlations of every image band. Consequently, as simulation results applied to real hyperspectral images demonstrate, the proposed method leads to a remarkable compression ratio and quality.