Iterated oversampled filter banks and wavelet frames

Ivan W. Selesnick, Levent Sendur

Research output: Contribution to journalConference articlepeer-review

Abstract

This paper takes up the design of wavelet tight frames that are analogous to Daubechies orthonormal wavelets - that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. The oversampled dyadic DWT considered in this paper is based on a single scaling function and two distinct wavelets. Having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale. As a result, the transform (like Kingsbury's dual-tree DWT) is nearly shift-invariant, and can be used to improve denoising. Because the associated time-frequency lattice preserves the dyadic structure of the critically sampled DWT (which the undecimated DWT does not) it can be used with tree-based denoising algorithms that exploit parent-child correlation.

Original languageEnglish (US)
Pages (from-to)733-744
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4119
DOIs
StatePublished - 2000
EventWavelet Applications in Signal and Image Processing VIII - San Diego, CA, USA
Duration: Jul 31 2000Aug 4 2000

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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