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Information × Registration Number 0211U005671, 0108U010843 , R & D reports Title Development and research of highly effective methods of processing of two-dimensional signals by blending wavelet-approximation popup.stage_title Head Lytvyn Oleg Mykolayovych, Доктор фізико-математичних наук Registration Date 20-12-2011 Organization Ukrainian Engineering-Pedagogic Academy popup.description2 Object of study – two-dimensional digital processing of signals. The research subject – digital processing of two-dimensional signals using blending wavelet approximation. Purpose – to develop and explore a method of approximate images of two-dimensional signals based on a blending wavelet approximation; develop and explore the method for solving the plane problem of Radon computed tomography (RCT) using projections and finite sums of Haar wavelets. Despite the considerable efficiency, modern computer tomography should be improved, as demonstrated artifacts – inclusion, shadows, which are no by investigated object. Therefore, the actual task is to develop new methods of mathematical modeling in computer tomography, which uses different scanning scheme than the existing ones. Wavelet analysis is a powerful alternative to Fourier analysis, primarily because of the wavelet transform to open up entirely new possibilities in signal and image processing. In this case, the problem of time consuming calculations recede into the background (especially with the growing power of computer technology). Wavelet signal processing provides the ability to fairly effective compression of signals and their restoration, low-loss information, and is used for problems of signal filtering. Therefore, the use of wavelets in computed tomography offers great opportunities for improvement of modern CT scanners: the development of new mechanisms for scanning and compression, and data presentation. Operators Haar wavelets blending approximation, which were investigated in the monography, O.M. Lytvyn, show a higher accuracy of the approximation, in comparison with the classical operators of wavelet approximations, or use a much smaller amount of data to restore the signals (images) with the required accuracy. We developed a new method for solving the plane problem of computed tomography using projection and finite sums of Haar wavelets. Important properties of the operators of the generalized two-dimensional wavelet approximation constructed on the basis of a blending wavelet approximation of functions of two variables is firstly that the error in the approximation of continuous functions is of the highest order of accuracy as the approximation of the multimodal wavelet approximation of functions of two variables; secondly the operators of the classical two-dimensional wavelet approximation required to achieve the same accuracy of the approximation is much more information about the approximated function than generalized two-dimensional wavelet approximation operators. This fact allows us to recommend them for practical data compression of two-dimensional signals (images) in modern image compression algorithms, such as compression has no analogues in the world. Product Description popup.authors Вязмітінова Оксана Олександрівна Гулік Людмила Іванівна Кулик Станіслав Іванович Литвин Олег Миколайович Литвин Олег Олегович Лобода Світлана Миколаївна Матвєєва Світлана Юріївна Нечуйвітер Олеся Петрівна Першина Юлія Ігорівна Хурдєй Євгенія Леонідівна Штепа Неля Ігорівна Ярмош Олена Віталіївна Ярова Ірина Анатоліївна popup.nrat_date 2020-04-02 Close