Fast computation of the continuous wavelet transform through oblique projections

Michael Vrhel, Chulhee Lee, Michael Unser

Research output: Contribution to journalConference article

7 Citations (Scopus)

Abstract

We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach achieves O(N) complexity per scale and the filter coefficients can be analytically obtained by a simple integration. Our method is to use P wavelets per octave and to approximate them with their oblique projection onto a space defined by a compact scaling function. The wavelet templates are expanded to larger sizes (octaves) using the two-scale relation and zero padded filtering. Error bounds are presented to justify the use of an oblique projection over an orthogonal one.

Original languageEnglish
Pages (from-to)1459-1462
Number of pages4
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
Publication statusPublished - 1996 Jan 1
EventProceedings of the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP. Part 1 (of 6) - Atlanta, GA, USA
Duration: 1996 May 71996 May 10

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octaves
wavelet analysis
Wavelet transforms
projection
templates
filters
scaling
coefficients

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

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Fast computation of the continuous wavelet transform through oblique projections. / Vrhel, Michael; Lee, Chulhee; Unser, Michael.

In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Vol. 3, 01.01.1996, p. 1459-1462.

Research output: Contribution to journalConference article

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AB - We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach achieves O(N) complexity per scale and the filter coefficients can be analytically obtained by a simple integration. Our method is to use P wavelets per octave and to approximate them with their oblique projection onto a space defined by a compact scaling function. The wavelet templates are expanded to larger sizes (octaves) using the two-scale relation and zero padded filtering. Error bounds are presented to justify the use of an oblique projection over an orthogonal one.

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