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Hyperspectral images formed by AVIRIS imager are often compressed for data transmission and storage. For this purpose, both lossless and lossy compression methods can be used, but the latter are able to provide considerably larger compression ratios. Lossy compression can be done effectively in automatic manner with grouping of sub-bands and setting the quantization step depending upon estimates of noise variance for sub-band images. In this paper we show how to select this quantization step for each group of sub-bands with providing a proper trade-off between losses (distortions) introduced and attainable compression ratio for simple and more realistic models of noise.