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26 March 1998 Fast implementation of wavelet transform for m-band filter banks
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Abstract
An orthogonal m-band discrete wavelet transform has an O(m2) complexity. In this paper, we present a fast implementation of such a discrete wavelet transform. In an orthonormal m-band wavelet system, the vanishing moments and orthogonality conditions are imposed on the scaling filter only. Given a scaling filter, one can design the other m-1 wavelet filters. It is well-known that there are infinitely many solutions in such designing procedure. Here we choose one specific type of solutions and implement the corresponding wavelet transform in a scheme which has complexity O(m). Thus for any scaling filter, one can always construct a full orthogonal m-band wavelet matrix with an O(m) discrete wavelet transform.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Jun Tian and Raymond O. Wells Jr. "Fast implementation of wavelet transform for m-band filter banks", Proc. SPIE 3391, Wavelet Applications V, (26 March 1998); https://doi.org/10.1117/12.304902
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