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

Bogdan Dumitrescu; Ilker Bayram; Ivan W. Selesnick

doi:10.1109/LSP.2007.913609

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

Bogdan Dumitrescu, Ilker Bayram, Ivan W. Selesnick

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	146-149
Number of pages	4
Journal	IEEE Signal Processing Letters
Volume	15
DOIs	https://doi.org/10.1109/LSP.2007.913609
State	Published - 2008

Keywords

Complex wavelet
Hilbert pair
Orthogonal filter banks
Positive trigonometric polynomials

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

Access to Document

10.1109/LSP.2007.913609

Cite this

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title = "Optimization of symmetric self-hilbertian filters for the dual-tree complex wavelet transform",

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.",

keywords = "Complex wavelet, Hilbert pair, Orthogonal filter banks, Positive trigonometric polynomials",

author = "Bogdan Dumitrescu and Ilker Bayram and Selesnick, {Ivan W.}",

note = "Funding Information: Manuscript received June 1, 2007; revised October 25, 2007. This work was supported by the Academy of Finland, under Project No. 213462, Finnish Centre of Excellence program (2006–2011). The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Gerald Matz.",

year = "2008",

doi = "10.1109/LSP.2007.913609",

language = "English (US)",

volume = "15",

pages = "146--149",

journal = "IEEE Signal Processing Letters",

issn = "1070-9908",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - JOUR

T1 - Optimization of symmetric self-hilbertian filters for the dual-tree complex wavelet transform

AU - Dumitrescu, Bogdan

AU - Bayram, Ilker

AU - Selesnick, Ivan W.

N1 - Funding Information: Manuscript received June 1, 2007; revised October 25, 2007. This work was supported by the Academy of Finland, under Project No. 213462, Finnish Centre of Excellence program (2006–2011). The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Gerald Matz.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Complex wavelet

KW - Hilbert pair

KW - Orthogonal filter banks

KW - Positive trigonometric polynomials

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DO - 10.1109/LSP.2007.913609

M3 - Article

AN - SCOPUS:67650180219

SN - 1070-9908

VL - 15

SP - 146

EP - 149

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this