Rational multiresolution analysis and fast wavelet transform: application to wavelet shrinkage denoising

This paper presents a contribution to rational multiresolution analysis (MRA). The rational analysis allows a better adaptation of scale factors to signal components than the dyadic one. The theory of rational MRA is reviewed and a pyramidal algorithm for fast rational orthogonal wavelet transform is proposed. Both, the analysis and synthesis parts of the process are detailed. Examples of scaling and wavelet functions and associated filters are given. Moreover, dealing with filters defined in Fourier domain, the implementation of the algorithm in this domain is described. Then, the study is extended to the 2D separable case in order to give a more conclusive presentation of the rational MRA. In order to illustrate the potential of rational analysis for signal and image processing, some results given by wavelet shrinkage denoising based on the 'SURE' thresholding method are presented. (C) 2004 Elsevier B.V. All rights reserved.