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We present a new low-complexity algorithm for hyperspectral image compression that uses linear prediction in the spectral domain. We introduce a simple heuristic to estimate the performance of the linear predictor from a pixel spatial context and a context modeling mechanism with one-band look-ahead capability, which improves the overall compression with marginal usage of additional memory. The proposed method is suitable to spacecraft on-board implementation, where limited hardware and low power consumption are key requirements. Finally, we present a least-squares optimized linear prediction technique that achieves better compression on data cubes acquired by the NASA JPL Airborne Visible/Infrared Imaging Spectrometer (AVIRIS).