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Lossy compression of AVIRIS hyperspectral images is considered. An automatic approach to selection of compression parameters depending on noise characteristics in component images is proposed. Several ways of performing lossy compression are discussed and compared. It is shown that in order to minimize distortions and provide a sufficient compression ratio it is reasonable to group the channels according to the evaluated noise variances in subband images and depending upon the sensor that produces sets of subband images. It is shown that for real life images the attained compression ratios can be of the order 8. ..25.