Analytic wavelets generated by radial functions Academic Article uri icon


  • 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.

published proceedings


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