- An efficient method and system for compressive sensing of hyperspectral data is presented. Compression efficiency is achieved by randomly encoding both the spatial and the spectral domains of the hyperspectral datacube. Separable sensing architecture is used to reduce the computational complexity associated with the compressive sensing of a large volume of data, which is typical of hyperspectral imaging. The system enables optimizing the ratio between the spatial and the spectral compression sensing ratios. The method is demonstrated by simulations performed on real hyperspectral data.