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Comparison of Algorithms for the Fast Computation of the Continuous Wavelet Transform

M.J. Vrhel, C. Lee, M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing IV, Denver CO, USA, August 6-9, 1996, vol. 2825, part I, pp. 422-431.



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 straightforward 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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