Journal of Fourier Analysis and Applications

, Volume 21, Issue 3, pp 509–553

Wavelets Centered on a Knot Sequence: Theory, Construction, and Applications

  • Bruce W. Anderson
  • Derek O. Bruff
  • Jeffrey S. Geronimo
  • Douglas P. Hardin
Article

DOI: 10.1007/s00041-014-9375-9

Cite this article as:
Anderson, B.W., Bruff, D.O., Geronimo, J.S. et al. J Fourier Anal Appl (2015) 21: 509. doi:10.1007/s00041-014-9375-9

Abstract

We develop a general notion of orthogonal wavelets ‘centered’ on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these schemes and apply them to a data set extracted from an ocelot image. As another application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the \(\tau \)-integers where \(\tau \) is the golden ratio. The resulting spaces then generate a multiresolution analysis of \(L^2(\mathbf {R})\) with scaling factor \(\tau \).

Keywords

Piecewise polynomial orthogonal wavelets Irregular knot sequences Quasi-crystal lattice Numerical algorithm 

Mathematics Subject Classification

42C40 65T60 33CA45 41A15 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Bruce W. Anderson
    • 1
  • Derek O. Bruff
    • 2
  • Jeffrey S. Geronimo
    • 3
  • Douglas P. Hardin
    • 2
  1. 1.BirminghamUSA
  2. 2.NashvilleUSA
  3. 3.AtlantaUSA

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