Periodic and Spline Multiresolution Analysis and the Lifting Scheme

  • Jürgen Prestin
  • Ewald Quak
Part of the Mathematics and Visualization book series (MATHVISUAL)


The lifting scheme is a well-known general framework for the construction of wavelets, especially in finitedimensional settings. After a short introduction about the basics of lifting, we discuss how wavelet constructions, in two specific finite settings, can be related to the lifting approach. These examples concern, on the one hand, polynomial splines and, on the other, the Fourier approach for translation-invariant spaces of periodic functions.


Space Versus Discrete Fourier Transform Lift Scheme Biorthogonal Wavelet Polynomial Spline 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jürgen Prestin
    • 1
  • Ewald Quak
    • 2
  1. 1.Institute of MathematicsUniversity of LübeckGermany
  2. 2.Department of Applied MathematicsSINTEF ICTOsloNorway

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