The WaveD Transform in R: Performs Fast Translation-Invariant Wavelet Deconvolution

Abstract

This paper provides an introduction to a software package called waved making available all code necessary for reproducing the figures in the recently published articles on the WaveD transform for wavelet deconvolution of noisy signals. 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 tne 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.