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Fast Continuous Wavelet Transform: A Least-Squares Formulation

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

Signal Processing, vol. 57, no. 2, pp. 103-119, March 1997.

We introduce a general framework for the efficient computation of the real continuous wavelet transform (CWT) using a filter bank. The method allows arbitrary sampling along the scale axis, and achieves O(N) complexity per scale where N is the length of the signal. Previous algorithms that calculated non-dyadic samples along the scale axis had O(Nlog(N)) computations per scale. Our approach approximates the analysing wavelet by its orthogonal projection (least-squares solution) onto a space defined by a compactly supported scaling function. We discuss the theory which uses a duality principle and recursive digital filtering for rapid calculation of the CWT. We derive error bounds on the wavelet approximation and show how to obtain any desired level of accuracy through the use of longer filters. Finally, we present examples of implementation for real symmetric and anti-symmetric wavelets.

AUTHOR="Vrhel, M.J. and Lee, C. and Unser, M.",
TITLE="Fast Continuous Wavelet Transform: {A} Least-Squares
JOURNAL="Signal Processing",

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