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Fast Computation of the Continuous Wavelet Transform through Oblique Projections

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

Proceedings of the Twenty-First IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'96), Atlanta GA, USA, May 7-9, 1996, vol. III, pp. 1459–1462.

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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