Comparison of algorithms for the fast computation of the continuous wavelet transform

Michael J. Vrhel; Chulhee Lee; Michael A. Unser

doi:10.1117/12.255253

Comparison of algorithms for the fast computation of the continuous wavelet transform

Michael J. Vrhel, Chulhee Lee, Michael A. Unser

Department of Electrical and Electronic Engineering

Research output: Contribution to journal › Conference article › peer-review

5 Citations (Scopus)

Abstract

We introduce a general framework for computing the continuous wavelet transform (CWT). Included in this framework is an FFT implementation as well as fast algorithms which achieve O(1) complexity per wavelet coefficient. The general approach that we present allows a straight forward comparison among a large variety of implementations. In our framework, computation of the CWT is viewed as convolving the input signal with wavelet templates that are the oblique projection of the ideal wavelets into one subspace orthogonal to a second subspace. We present this idea and discuss and compare particular implementations.

Original language	English
Pages (from-to)	422-431
Number of pages	10
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	2825
DOIs	https://doi.org/10.1117/12.255253
Publication status	Published - 1996
Event	Wavelet Applications in Signal and Image Processing IV - Denver, CO, United States Duration: 1996 Aug 6 → 1996 Aug 6

All Science Journal Classification (ASJC) codes

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

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10.1117/12.255253

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abstract = "We introduce a general framework for computing the continuous wavelet transform (CWT). Included in this framework is an FFT implementation as well as fast algorithms which achieve O(1) complexity per wavelet coefficient. The general approach that we present allows a straight forward comparison among a large variety of implementations. In our framework, computation of the CWT is viewed as convolving the input signal with wavelet templates that are the oblique projection of the ideal wavelets into one subspace orthogonal to a second subspace. We present this idea and discuss and compare particular implementations.",

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T1 - Comparison of algorithms for the fast computation of the continuous wavelet transform

AU - Vrhel, Michael J.

AU - Lee, Chulhee

AU - Unser, Michael A.

PY - 1996

Y1 - 1996

N2 - We introduce a general framework for computing the continuous wavelet transform (CWT). Included in this framework is an FFT implementation as well as fast algorithms which achieve O(1) complexity per wavelet coefficient. The general approach that we present allows a straight forward comparison among a large variety of implementations. In our framework, computation of the CWT is viewed as convolving the input signal with wavelet templates that are the oblique projection of the ideal wavelets into one subspace orthogonal to a second subspace. We present this idea and discuss and compare particular implementations.

AB - We introduce a general framework for computing the continuous wavelet transform (CWT). Included in this framework is an FFT implementation as well as fast algorithms which achieve O(1) complexity per wavelet coefficient. The general approach that we present allows a straight forward comparison among a large variety of implementations. In our framework, computation of the CWT is viewed as convolving the input signal with wavelet templates that are the oblique projection of the ideal wavelets into one subspace orthogonal to a second subspace. We present this idea and discuss and compare particular implementations.

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EP - 431

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

T2 - Wavelet Applications in Signal and Image Processing IV

Y2 - 6 August 1996 through 6 August 1996

ER -

Comparison of algorithms for the fast computation of the continuous wavelet transform

Abstract

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