The paper proposes a solution to the problem of minimizing the number of standards in order to increase both the compression coefficient of hyperspectral images (HSI) and the speed of correlation extreme compression methods (CEM). As modifications of the CEM, randomized and differential compression algorithms are offered. The randomized and difference algorithms are based on the hypothesis of spatial compactness of pixels located in local regions of the image matrix. This means that when a new template is formed based on an unrecognized pixel, there is a high probability of using a pixel that lies near the boundaries of the coverage areas of the existing templates, which leads to their increase. In order to reduce the influence of spatial compactness of pixels on the formation of standards, a methodology based on changing the sequence of recognized pixels is proposed. In a randomized algorithm, a row of the matrix is randomly determined for this, on the basis of which a sequence of recognized pixels is generated by a random column generator. In the difference algorithm of compression, the row number of the matrix is determined by the rule for finding the members of an arithmetic progression with a given difference. For the selected line a sequence of recognizable pixels is formed on the same principle. It should be noted that line-by-line pixel recognition in the self-learning mode allows compressing HSI of almost any volume. The effectiveness of the created algorithms is demonstrated on two fragments of real HSI. A comparative analysis of all three compression algorithms in terms of the quantitative composition of the obtained standards is presented.