The WaveD Transform in R: performs fast translation-invariant wavelet deconvolution.

Marc Raimondo and Michael Stewart

Abstract

This paper provides an introduction to a software package called 'waved' that works within the statistical environment R making available all code necessary for reproducing the figures in the recently published articles on the WaveD method for Wavelet Deconvolution of noisy signals, Johnstone, Kerkyacharian, Picard and Raimondo (2004). The forward WaveD transforms and their inverses can be computed using any wavelet from the Meyer family. The WaveD coefficients can be depicted according to time and resolution in several ways for data analysis. The algorithm which implements the translation invariant WaveD transform takes full advantage of the Fast Fourier Transform (FFT) and runs in O(n(\log n)²) steps only. The 'waved' package includes functions to perform thresholding and fine resolution tuning according to methods in the literature as well as newly designed visual and statistical tools for assessing WaveD fits. We give a 'waved' tutorial session and review benchmark examples of noisy convolutions to illustrate the non-linear adaptive properties of wavelet deconvolution.

Keywords: R-packages, WaveD method, WVD, deconvolution, Meyer wavelet.

AMS Subject Classification: Primary 62G20.