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

23 October 1996 Comparison of algorithms for the fast computation of the continuous wavelet transform

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

Author Affiliations +

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255253
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

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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Michael J. Vrhel, Chulhee Lee, and Michael A. Unser "Comparison of algorithms for the fast computation of the continuous wavelet transform", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255253

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