Fast implementation of wavelet transform for m-band filter banks
Jun Tian, Raymond O. Wells · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
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.