The work is a continuation of the authors' research on the problem of adaptive compression of raster hyperspectral images of Earth remote sensing. In the first part of the article, the authors give an overview of the current state of affairs in the processing of images of remote sensing of the Earth, the characteristic properties of raster hyperspectral images in the context of the prospects for lossy compression, the problems of the effectiveness of existing compression methods of this type of graphic documents are indicated. Further, the article highlights the issues of increasing the efficiency of methods for eliminating information redundancy of raster hyperspectral images of Earth remote sensing. The problems of designing and creating parallel methods and algorithms for the compression of raster hyperspectral ERS images are considered. A method for the development of a parallel algorithm for constructing a system of local homogeneous "well-adapted" basis functions for raster hyperspectral images, based on the Chebyshev approximation for systems using the CUDA graphics processor, is proposed.