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Num. Meth. Prog., 2008, Volume 9, Issue 1, Pages 84–89 (Mi vmp421)  

Вычислительные методы и приложения

The representation of a wavelet transform of the Gaussian family by a superposition of solutions to partial differential equations

E. B. Postnikov

Kursk State University

Abstract: The usage of partial differential equations for the evaluation of a wavelet transform with real and complex wavelets and with vanishing higher moments is considered. Contrary to the case of the transform with the standard Morlet wavelet, the sought-for transform can be found as a superposition of solutions to several Cauchy problems with various initial values. These initial values are the products of a transformed function with some power functions whose exponents vary from zero to the maximal number of a vanishing moment.

Keywords: continuous wavelet transform, Morlet wavelet, Gaussian wavelets, diffusion equation, partial differential equations.

Full text: PDF file (1426 kB)
UDC: 517.955:517.444

Citation: E. B. Postnikov, “The representation of a wavelet transform of the Gaussian family by a superposition of solutions to partial differential equations”, Num. Meth. Prog., 9:1 (2008), 84–89

Citation in format AMSBIB
\Bibitem{Pos08}
\by E.~B.~Postnikov
\paper The representation of a wavelet transform of the Gaussian family by a superposition of solutions to partial differential equations
\jour Num. Meth. Prog.
\yr 2008
\vol 9
\issue 1
\pages 84--89
\mathnet{http://mi.mathnet.ru/vmp421}


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