Smooth Wavelet Tight Frames with Zero Moments

Research output: Contribution to journalArticle

Abstract

This paper considers the design of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. In particular, this paper takes up the design of systems 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. Gröbner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-tree DWT of Kingsbury, one goal is to achieve near shift invariance while keeping the redundancy factor bounded by 2, instead of allowing it to grow as it does for the undecimated DWT (which is exactly shift invariant). Like the dual tree, the overcomplete DWT described in this paper is less shift-sensitive than an orthonormal wavelet basis. Like the examples of Chui and He, and Ron and Shen, the wavelets are much smoother than what is possible in the orthonormal case.

Original languageEnglish (US)
Pages (from-to)163-181
Number of pages19
JournalApplied and Computational Harmonic Analysis
Volume10
Issue number2
DOIs
StatePublished - Mar 2001

Fingerprint

Wavelet Frames
Tight Frame
Orthonormal
Moment
Wavelets
Zero
Wavelet Bases
Filter Banks
Filter banks
Invariance
Redundancy
Smoothness
Design
Polynomials
Filter
Polynomial
Invariant

Keywords

  • Overcomplete signal expansions; wavelets; frames

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Smooth Wavelet Tight Frames with Zero Moments. / Selesnick, Ivan.

In: Applied and Computational Harmonic Analysis, Vol. 10, No. 2, 03.2001, p. 163-181.

Research output: Contribution to journalArticle

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