Geodesic
The representation of a wavelet transform of the Gaussian family by a superposition of solutions to partial differential equations
Numerical methods and programming, Tome 9 (2008) no. 1, pp. 84-89.

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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, partial differential equations.
Mots-clés : diffusion equation 
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     author = {E. B. Postnikov},
     title = {The representation of a wavelet transform of the {Gaussian} family by a superposition of solutions to partial differential equations},
     journal = {Numerical methods and programming},
     pages = {84--89},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2008_9_1_a10/}
}
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E. B. Postnikov. The representation of a wavelet transform of the Gaussian family by a superposition of solutions to partial differential equations. Numerical methods and programming, Tome 9 (2008) no. 1, pp. 84-89. http://geodesic.mathdoc.fr/item/VMP_2008_9_1_a10/