Abstract
The article is devoted to an algorithm for finding the values of smooth biorthogonal wavelets and their partial derivatives, constructed using lazy wavelet lifting schemes, which are successfully used for signal processing, information compression, and solutions to differential and integral equations of computer geometry. It is based on various forms that allow one to obtain biorthogonal components with desired properties: smoothness, symmetry, compactness of the carrier. The algorithms under consideration are based on the convolution transformation, the presence of fast cascade algorithms for finding the coefficients of the wavelet expansion of a function allows, limited to a small number of terms in the expansion, to obtain fairly accurate approximations of the function. By specifying a mask that leads to the desired properties of the limit function, scaling functions with the required properties are obtained. Achieving the desired properties of wavelets is directly related to stationary subdivision schemes. Many of the frequently used wavelets, for example, spline wavelets, Daubechies wavelets, have a compact medium, therefore they are executed quickly in modern libraries written for programming languages. The calculations used the TensorFlow library, written for the Phyton programming language.
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Deniskina, G.Y., Deniskin, Y.I., Bityukov, Y.I. (2021). About Biortogonal Wavelets, Created on the Basis of Scheme of Increasing of Lazy Wavelets. In: Radionov, A.A., Gasiyarov, V.R. (eds) Advances in Automation II. RusAutoCon 2020. Lecture Notes in Electrical Engineering, vol 729. Springer, Cham. https://doi.org/10.1007/978-3-030-71119-1_18
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