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 <i>O</i>(n(log n)<sup>2</sup>)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.
Highlights
In this paper we present the WaveD transform in R and illustrate some statistical applications of the WaveD transform to the deconvolution of noisy signals
Ξ, ζ are independent white noises and 0 < ε, ǫ < 1 are noise levels. Both f and g are supposed to be periodic on T and g ∗ f (t) denotes the circular convolution
Earlier versions of the WaveD method have been implemented through various small Matlab packages, corresponding to various existing WaveD transforms
Summary
In this paper we present the WaveD transform in R and illustrate some statistical applications of the WaveD transform to the deconvolution of noisy signals. The aim of deconvolution is to recover an unknown function f from a noisy observation of g ∗ f ,. Where the convolution kernel g is observed with or without noise, gǫ(t) = g(t) + ǫ ζ(t), t ∈ T = [0, 1],. Ξ, ζ are independent white noises and 0 < ε, ǫ < 1 are noise levels Both f and g are supposed to be periodic on T and g ∗ f (t) denotes the circular convolution. An illustration of model (1) is given in Figure 3 using the test functions of Figure 1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
