Wavelet transforms generated by splines

Amir Z. Averbuch, Valery A. Zheludev

Research output: Contribution to journalArticlepeer-review


In this paper, we design a new family of biorthogonal wavelet transforms that are based on polynomial and discrete splines. The wavelet transforms are constructed via lifting steps, where the prediction and update filters are derived from various types of interpolatory and quasi-interpolatory splines. The transforms use finite and infinite impulse response (IIR) filters and are implemented in a fast lifting mode. We analyze properties of the generated scaling functions and wavelets. In the case when the prediction filter is derived from a polynomial interpolatory spline of even order, the synthesis scaling function and wavelet are splines of the same order. We formulate conditions for the IIR filter to generate an exponentially decaying scaling function.

Original languageEnglish
Pages (from-to)257-291
Number of pages35
JournalInternational Journal of Wavelets, Multiresolution and Information Processing
Issue number2
StatePublished - Mar 2007


  • Filter
  • Lifting
  • Spline
  • Subdivision
  • Wavelet


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