The dissertation is devoted to the solution of scientific problems of improving the level of digital image compression, through the development of information technology, based on the compression methods and the use of transformations, providing invariance of digital images. A mathematical model of analog realistic images is proposed, based on two-dimensional polynomial splines (B-splines) that are close to the average interpolation splines, which are having low computational complexity to be implemented in the software and allows taking into account method of recording images. The model allows us to consider digital images as a sequence set in a linear space that sets the input transformation to ensure invariance of digital images with simple computational point of view. The metric, based on experimental studies involving compression methods with losses, is proposed, which is a measure of image detail and on which the level of compression of digital images can be predicted. The known linear operators of filtration (one dimensional and two dimensional) are submitted, based on the introduced mathematical model of realistic digital images, satisfying the requirement of digital image processing in real time. Experimental studies of digital image compression based on compression methods with and without losses are done, with previous use of anti-aliasing low pass filter. Statistically proven that the use of transformations, providing invariance of digital images ("smoothing" - "contrast"), in combination with compression methods increases the compression level. The new operators are offered, which are pseudo inverse to the known low pass filters, which, unlike existing low pass filters, provide smaller error of reproduction of digital image after smoothing. Also, the experimental studies of new operators, which are pseudo inverse to the known low pass filters, which, unlike existing low pass filters, provide smaller error of reproduction of digital image after smoothing. Statistically proven that the use of specified pseudo inverse (contrast) filters provides better results of reproduction of digital images, corrupted by appropriate low-pass filter. The new information technology is developed, which includes the transformations, which provide the invariance of digital images and compression methods. The software that implements them is developed. The informational technology of increasing the compression level of digital images is developed. On the first step it scores the image processing, using low filtering methods with varying degrees of smoothing the original image. On the second step the compression with any method or compression algorithm is implemented, preserving the format of compressed image. Further it also provides decompression and overlay of the pseudo inverse filter. Experimental studies of the proposed information technology of improvement of the compression level of digital images are provided, using the samples of digital images and with the assistance of independent users. A description of the developed software for the implementation of the proposed information technology of improvement of the compression level of digital images and circuits, diagrams and the user's manual are provided. This information technology also enables: zoom, aliquot scale analysis, digital stabilization, high-frequency filtering, changing of the color representation system, compression with methods of archiving, compression with lossy compression methods, receiving the statistical data of the processed image. The main results of the dissertation are introduced in institutions and organizations.
