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This paper proposes a preprocessing algorithm for aerospace hyperspectral images based on a mathematical apparatus effectively applied in pre-compression transformation problems. In particular, several methods have been analyzed for hyperspectral image (signal) preprocessing from the point of view of digital signal processing algorithms. These mathematical methods are used for problems of filtering signals from noise of different natures and for compression and restoration of signals after their transmission through communication channels. The results of comparative analysis of preparatory processing of lossy compression algorithms based on wavelet analysis, discrete and orthogonal transforms are also given, demonstrating minimization of loss level of reconstructed decoded images. The performance of the proposed preprocessing algorithms with quality metrics is presented to evaluate the quality of the reconstructed hyperspectral aerospace images. The results of this study can be applied and used in the tasks of special processing of hyperspectral images, as well as fundamental knowledge of mathematical apparatuses of the proposed orthogonal preprocessing, considering the specificity of the data which is very important in obtaining images ready for compression for the subsequent identification of objects of the Earth's surface and using such mathematical transformations at the hyperspectral image preprocessing stage before compression provides efficient archiving of the obtained data, while reducing the communication channel load. Through the use of quality metrics of the reconstructed images, the preprocessing algorithm provides an understanding of the threshold of the peak signal-to-noise ratio value and the efficiency of its application to calculate and minimize the loss rate. [ABSTRACT FROM AUTHOR]