Rapid computation of the continuous wavelet transform by oblique projections

We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach has the following attractive features: it achieves O(N) complexity per scale, the filter coefficients can be analytically obtained by a simple integration, and the algorithm is faster than a least squares approach with negligible loss in accuracy. Our method is to use P wavelets per octave and to approximate them with their oblique projection onto a space defined by a compactly supported 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. All the filters are FIR with the exception of one filter, which is implemented using a fast recursive algorithm.