Fast integral wavelet transform on a dense set of the time-scale domain

Abstract

The objective of this paper is to introduce a fast algorithm for computing the integral wavelet transform (IWT) on a dense set of points in the time-scale domain. By applying the duality principle and using a compactly supported splinewavelet as the analyzing wavelet, this fast integral wavelet transform (FIWT) is realized by applying only FIR (moving average) operations, and can be implemented in parallel. Since this computational procedure is based on a local optimal-order spline interpolation scheme and the FIR filters are exact, the IWT values so obtained are guaranteed to have zero moments up to the order of the cardinal spline functions. The semi-orthogonal (s.o.) spline-wavelets used here cannot be replaced by any other biorthogonal wavelet (spline or otherwise) which is not s.o., since the duality principle must be applied to some subspace of the multiresolution analysis under consideration. In contrast with the existing procedures based on direct numerical integration or an FFT-based multi-voice per octave scheme, the computational complexity of our FIWT algorithm does not increase with the increasing number of values of the scale parameter.Mathematics Subject Classification (1991): 41A05, 41A15, 65R10

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