ПРИМЕНЕНИЕ ТЕОРИИ ВЕЙВЛЕТОВ ПРИ СЖАТИИ И ФИЛЬТРАЦИИ ГЕОИНФОРМАЦИИ

Abstract

The purpose of the article is to develop a detailed and accessible technology for the application of wavelets in the processing of geo-information, the subject of research is wavelet-based filtering and compression of geo-information. The research methodology is based on the modern theory of wavelets in the light of linear algebra. Research methods involve study and generalization, abstraction, formalization, mathematical modeling using computer programs compiled by the authors.After the introduction and formulation of the problem, the basic positions of linear algebra are presented, on which the content of the article is based when constructing orthonormal bases in one- and two-dimensional cases. First, the application of the general theory to the decomposition of the vector of initial data in the Haar and Shannon bases is given. Further, on the basis of the Haar basis, orthonormal bases of wavelet transforms and filtering information are constructed. The procedure for creating wavelet filters by a sequence of convolutions, the use of MSA analysis for constructing an orthonormal basis of the wavelet transform is considered. Implemented the practical possibility of wavelet filtering based on specific programs for modeling geo-information data fields and images, data compression and filtering. The result of the work is the methods of constructing orthonormal bases by various methods of wavelet transform, based on which algorithms and corresponding computer programs for geoinformation compression are compiled using the example of terrain and photographic images. The efficiency of geoinformation compression and noise filtering using wavelets was investigated. A method has been developed for determining the value of a filter depending on the accuracy of the initial geo-information, illustrated by the example of calculating the filter value for compressing information about the heights of the terrain. The same technique is recommended for image filtering.