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Two automatic approaches to lossy compression of hyperspectral AVIRIS images are proposed and considered. A first approach (strategy) is to filter images on-board and then to transfer compressed. A second strategy assumes that image filtering is performed on-land applied to decompressed data. In both cases, blind evaluation of noise variance is carried out. For both strategies, sub-band images can be compressed component-wise or adaptively grouped and compressed using a modified 3D DCT based coder. It is shown that the latter (3D) technique provides considerably better results. The first strategy produces wider facilities of hyperspectral image manipulation on-land whilst for the second strategy larger compression ratio can be automatically provided. This is demonstrated for a set of real life AVIRIS images.