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 ℝs is large. Thus projecting a functionf 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.
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Communicated by R.A. DeVore
Supported by NSF Grant #DMS-92-06928, Air Force Grant #F49620-92-J-0403DEF and NATO Grant #CR-900158.
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Chui, C.K., Stöckler, J. & Ward, J.D. Analytic wavelets generated by radial functions. Adv Comput Math 5, 95–123 (1996). https://doi.org/10.1007/BF02124736
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DOI: https://doi.org/10.1007/BF02124736
Keywords
- Analytic wavelet
- non-stationary wavelet
- radial function
- shift-invariant space
- time-frequency window
- Littlewood-Paley identity