FAST CONTINUOUS WAVELET TRANSFORM - A LEAST-SQUARES FORMULATION

We introduce a general framework for the efficient computation of the real continuous wavelet transform (CWT) using a filter bank. The metho d allows arbitrary sampling along the scale axis, and achieves O(N) co mplexity per scale where N is the length of the signal. Previous algor ithms that calculated non-dyadic samples along the scale axis had O(N log(N)) computations per scale. Our approach approximates the analyzin g wavelet by its orthogonal projection (least-squares solution) onto a space defined by a compactly supported scaling function. We discuss t he theory which uses a duality principle and recursive digital filteri ng for rapid calculation of the CWT. We derive error bounds on the wav elet approximation and show how to obtain any desired level of accurac y through the use of longer filters. Finally, we present examples of i mplementation for real symmetric and anti-symmetric wavelets. (C) 1997 Published by Elsevier Science B.V.