The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use of large amounts of spatial data, efficient storage of data on on-board recording media and their transmission via communication channels. This leads to the need to create new effective methods of compression and data transmission of remote sensing of the Earth. The possibility of using fractal functions for image processing, which were transmitted via the satellite radio channel of a spacecraft, is considered. The information obtained by such a system is presented in the form of aerospace images that need to be processed and analyzed in order to obtain information about the objects that are displayed. An algorithm for constructing image encoding–decoding using a class of continuous functions that depend on a finite set of parameters and have fractal properties is investigated. The mathematical model used in fractal image compression is called a system of iterative functions. The encoding process is time consuming because it performs a large number of transformations and mathematical calculations. However, due to this, a high degree of image compression is achieved. This class of functions has an interesting property—knowing the initial sets of numbers, we can easily calculate the value of the function, but when the values of the function are known, it is very difficult to return the initial set of values, because there are a huge number of such combinations. Therefore, in order to de-encode the image, it is necessary to know fractal codes that will help to restore the raster image.

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Our paper describes the methodology of an effective system construction based on information systems self-diagnosis using the case of Ukrainian enterprises in metallurgy, energy, and chemical industry. It describes the method of organization and implementation of self-diagnosis, mechanisms of detection, as well as the identification and localization of failed modules. The results formulate the criteria of sufficiency of efficiency of diagnostic information in the absence of restrictions on performance of elementary checks. Moreover, it yields the criterion of sufficiency of diagnostic information in the presence of restrictions on performance of elementary checks.

The rapid growth of geo-information technology capabilities in the field of spatial data processing and analysis has led to a significant growth of the role of geo-information systems in different areas of human activity. Application of approaches to spatial information processing from satellites new for more effective and efficient assessment of the state of plant cover is caused by growing tendency of availability to data of Earth remote sensing. The article offers an information system that allows to quickly and conveniently track changes in the vegetation. The analysis was carried out on the example of the Chornobyl Area between 2000 and 2020. The Chornobyl Disaster coincides with the period of intensive vegetative plant development. During that period, they are most sensitive to radiation. It has been established that for defining the quantitative state of biomass the NDVI index at different time intervals is most often used. But this index becomes ineffective during periods of weakening of active phase of vegetation. This is therefore of practical interest to assess the possibility of using the K-means clustering for the analysis of space images of vegetation cover at different phases of vegetation. As a result of the research, water surface, land with and without vegetation has been correctly interpreted, thus determining the land with a sparse vegetation and dense vegetation cover. The maps of the vegetation cover according to the normalized vegetative index using the K-medium method were constructed, the method by which changes in vegetation over 20 years can be clearly observed. The accuracy results were verified with the Common Method Bias. According to the calculations, despite all natural cataclysms (temperature increase, drought, winter anomalies of precipitations and temperatures, storms, forest fires), as well as human activity (sanitary clear cuttings, illegal logging), vegetation in the Chornobyl zone continues to grow and its areas will increase, although not so quickly.

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