EXACT RECONSTRUCTION ALGORITHMS FOR THE DISCRETE WAVELET TRANSFORM USING SPLINE-WAVELETS

By making a discrete finite time signal periodic, it is shown that nonorthogonal B-spline wavelets can be used in a discrete wavelet transform with exact decomposition and reconstruction. A nonrecursive algorithm using only Finite Impulse Response filters (FIR) with complexity O(N-2) is presented. The complexity is reduced to O(N log(2) N) by using Fast Fourier Transforms (FFT). A faster algorithm is obtained by using recursive filters in the decomposition or reconstruction of the signal. The recursive algorithm has complexity O(N), and the same accuracy as the others. By allowing nonsymmetric wavelets, an exact orthogonal reconstruction algorithm is shown, which also has complexity O(N). (C) 1995 Academic Press, Inc