Fast computation of the continuous wavelet transform through oblique projections
Michael J. Vrhel, Chulhee Lee, Michael A. Unser · 2002
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.