A new approach (designed to lower computational complexity) to compression of finite binary data, based on the application of “exclusive-or” operation, is presented in the paper. The new concept of an identifying sequence, associated with a particular decomposition scheme, is introduced. A new heuristic algorithm for calculation of the identifying sequences has been developed. Two robust algorithms – for compressing and streaming the sequences (using a priori compiled decomposition tables), and for real time decoding of the compressed streams – were proposed and implemented. The experimental results confirmed that the developed approach gave a data compression effect on an ordinary computer system.

This Master degree paper analyses hyperbolic image filtering in spaces of different dimensionality. It investigates the problem of optimal filtering space selection. Several popular image compression methods (both lossless and lossy) are reviewed. This paper analyses the problems of image smoothness parameter discovering, image dimensionality changing, hyperbolic image filtering and filtering efficiency evaluation and provides the solution methods of the problems. Schemes for the experimental examination of theoretical propositions and hypotheses are prepared. This paper comprehensively describes experiments with one-, two- and threedimensional images and the results of the experiments. Conclusions about the efficiency of hyperbolic image filtering in other than "native" image space are based on the results of the experiments. The criterion for the selection of optimal image filtering space is evaluated. Guidelines for further research are also discussed. The presentation Specific Features of Hyperbolic Image Filtering, which was based on this Master degree paper, was made at the conference Mathematics and Mathematical Modeling (KTU – 2004). This text is available in appendixes.