Optimization of symmetric self-hilbertian filters for the dual-tree complex wavelet transform

Bogdan Dumitrescu, Ilker Bayram, Ivan Selesnick

Research output: Contribution to journalArticle

Abstract

In this letter, we expand upon the method of Tay for the design of orthonormal ldquoQ-shiftrdquo filters for the dual-tree complex wavelet transform. The method of Tay searches for good Hilbert-pairs in a one-parameter family of conjugate-quadrature filters that have one vanishing moment less than the Daubechies conjugate-quadrature filters (CQFs). In this letter, we compute feasible sets for one- and two-parameter families of CQFs by employing the trace parameterization of nonnegative trigonometric polynomials and semidefinite programming. This permits the design of CQF pairs that define complex wavelets that are more nearly analytic, yet still have a high number of vanishing moments.

Original languageEnglish (US)
Pages (from-to)146-149
Number of pages4
JournalIEEE Signal Processing Letters
Volume15
DOIs
StatePublished - 2008

Fingerprint

Wavelet transforms
Wavelet Transform
Quadrature
Filter
Optimization
Vanishing Moments
Parameterization
Polynomials
Trigonometric Polynomial
Semidefinite Programming
Orthonormal
Hilbert
Expand
Two Parameters
Wavelets
Non-negative
Trace
Family
Design

Keywords

  • Complex wavelet
  • Hilbert pair
  • Orthogonal filter banks
  • Positive trigonometric polynomials

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Applied Mathematics

Cite this

Optimization of symmetric self-hilbertian filters for the dual-tree complex wavelet transform. / Dumitrescu, Bogdan; Bayram, Ilker; Selesnick, Ivan.

In: IEEE Signal Processing Letters, Vol. 15, 2008, p. 146-149.

Research output: Contribution to journalArticle

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