Analytic wavelets generated by radial functions Academic Article

abstract

• In this paper, we deal with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions. These radial basis functions are noted for their effectiveness in terms of "projection", such as interpolation and least-squares approximation, particularly when the data structure is scattered or the dimension of s is large. Thus projecting a function f onto a suitable multiresolution space is relatively easy here. The associated multiresolution spaces approximate sufficiently smooth functions exponentially fast. The non-stationary wavelets satisfy the Littlewood-Paley identity so that perfect reconstruction of wavelet decompositions is achieved. For the univariate case, we give a detailed analysis of the time-frequency localization of these wavelets. Two numerical examples for the detection of singularities with analytic wavelets are provided. J.C. Baltzer AG, Science Publishers.

authors

• Ward, Joseph

published proceedings

• ADVANCES IN COMPUTATIONAL MATHEMATICS

author list (cited authors)

• Chui, C. K., Stockler, J., & Ward, J. D.

citation count

• 30

complete list of authors

• Chui, CK||Stockler, J||Ward, JD

publication date

• December 1996

publisher

• Springer Nature  Publisher

published in

• Advances in Computational Mathematics  Journal

keywords

• Analytic Wavelet
• Littlewood-paley Identity
• Non-stationary Wavelet
• Radial Function
• Shift-invariant Space
• Time-frequency Window

Digital Object Identifier (DOI)

• 10.1007/BF02124736

start page

• 95

end page

• 123

volume

• 5

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fbf02124736