Kulyk S. Mathematical modeling in computerized tomography by wavelets

The dissertation is devoted to mathematical modelling in a computerized tomography by wavelets. The new method restoration of distribution of the inner structure of a three-dimensional body in the set plane by means of projections which arrive from a computer tomograph is offered and investigated. Operators of the generalized wavelet-approximation constructed on the basis of the blending wavelet-approximation are besides, offered and investigated. This generalized wavelet-approximation demands considerably smaller number of wavelet-factors for achievement of the set accuracy of restoration of two-dimensional images in comparison with classical two-dimensional wavelet-approximation. This fact can be used for more exact description of some classes of two-dimensional signals in digital processing of signals, or for use of smaller quantity of wavelet-factors at the set accuracy of the description of two-dimensional signals, in comparison with classical methods. Results can be used at digital processing of two-dimensional signals, and also at designing of computer tomographs of new type with original scanning scheme and processing data, arriving from a computer tomograph.