Rational wavelet transform: application to signal denoising

Abstract

This paper deals with the rational wavelet transform apply to a wavelet shrinkage problem. The rational multiresolution analysis (MRA) allows a better adaptation of the scale factor to the signal components than the dyadic one. The theory of the rational MRA is reviewed and a pyramidal algorithm for the computation of the fast orthogonal wavelet transform is proposed. Both, the analysis and the synthesis parts of the process are detailed. Moreover, using filters defined in Fourier domain, the implementation of the proposed algorithm is extended to this space. To illustrate the potential of rational analysis for signal processing, a wavelet shrinkage application is presented.