Hyperspectral imaging is known for its rich spatial-spectral information. The spectral bands provide the ability to distinguish substances spectra which is substantial for analyzing materials. However, highdimensional data volume of hyperspectal images is problematic for data storage. In this paper, we present a lossy hyperspectral image compression system based on the regression of 3D wavelet coefficients. The 3D wavelet transform is applied to sparsely represent the hyperspectral images (HSI). A support vector machine regression (SVR) is then applied on wavelet details and provides vector supports and weights which represent wavelet texture features. To achieve the best possible overall rate-distortion performance after regression, entropy encoding based on run-length encoding (RLE) and arithmetic encoding are used. To preserve the spatial pertinent information of the image, the lowest subband wavelet coefficients are furthermore encoded by a lossless coding with differential pulse code modulation (DPCM). Spectral and spatial redundancies are thus substantially reduced. Experimental tests are performed over several hyperspectral images from airborne and spaceborne sensors and compared with the main existing algorithms. The obtained results show that the proposed compression method has high performances in terms of rate-distortion and spectral fidelity. Indeed, high PSNRs and classification accuracies, which could exceed 40.65 dB and 75.8 % respectively, are observed for all decoded HSI images and overpass those given by