rwavelet

Wavelet Analysis

Download and Install

Install the devtools package if you haven’t already.

install.packages("devtools")

To install the development package, type the following at the R command line:

devtools::install_github("fabnavarro/rwavelet")
library(rwavelet)

To install the CRAN version of the package, type the following:

install.packages("rwavelet")

General features

• 1d, 2d and 3d MRA Forward/Inverse Wavelet Transforms Periodized Orthogonal (FWT_PO, IFWT_PO)
• 1d, 2d tensor Forward/Inverse Wavelet Transform Periodized Orthogonal (FTWT_PO, ITWT_PO)
• 1d, 2d Translation Invariant Forward/Inverse Wavelet Transform (FWT_TI, IWT_TI, also know as redundant wavelet transform, maximal overlap wavelet transform, undecimated wavelet transform or stationary wavelet transform)
• Linear wavelet estimation/approximation (using 2 fold cross validation, CVLinear)
• Non linear wavelet estimation/approximation (hard and soft thresholding, can be easily extended to other thresholding rules)
• 1d Wavelet Block Thresholding estimation/approximation
• …

To obtain the complete list of package functions, simply type

help(package = "rwavelet")

Getting Started

Here is an example of denoising of an experimental nuclear magnetic resonance (NMR) spectrum. We start by loading the data:

data("RaphNMR")
Y <- RaphNMR
n <- length(Y)
t <- seq(0, 1, length = n)

Then we specify the coarse decomposition scale $j_0$, the wavelets we want to use (here, Symmlet with 6 vanishing moments) and we perform a fast wavelet transform to get the noisy wavelet coefficients (Ywd):

j0 <- 0
J <- log2(n)
qmf <- MakeONFilter('Symmlet', 6)
Ywd <- FWT_PO(Y, j0, qmf)
Ywnoise <- Ywd

We estimate $\sigma$ the standard deviation of the noise using the maximum absolute deviation (with only the finest scale coefficients). We apply a hard thresholding rule (with a universal threshold) to the coefficient estimators and obtain the estimator by applying an inverse transform:

hatsigma <- MAD(Ywd[(2^(J-1)+1):2^J])
lambda <- sqrt(2*log(n))*hatsigma
Ywd[(2^(j0)+1):n] <- HardThresh(Ywd[(2^(j0)+1):n], lambda)
fhat <- IWT_PO(Ywd, j0, qmf)

Finally, we plot the resulting estimator:

par(mfrow=c(2,2), mgp = c(1.2, 0.5, 0), tcl = -0.2,
    mar = .1 + c(2.5,2.5,1,1), oma = c(0,0,0,0))
plot(t,Y,xlab="", ylab="", main="Observations")
plot(t,Y,xlab="", ylab="", main="Observations and Estimator")
matlines(t, fhat, lwd=2, col="blue", lty=1)
plot(Ywnoise, ylim=c(-20, 20), xlab="", ylab="", main = "Noisy Coefficients")
matlines(rep(lambda, n), lwd=2,col="red",lty=1)
matlines(-rep(lambda, n), lwd=2,col="red",lty=1)
plot(Ywd, ylim=c(-20,20), xlab="", ylab="", main = "Estimated Coefficients")

See the package vignette or documentation for more details. You could also build and see the vignette associated with the package using the following lines of code

devtools::install_github("fabnavarro/rwavelet", build_vignettes = TRUE)
library(rwavelet)

Then, to view the vignette

vignette("rwaveletvignette")

How to cite

citation("rwavelet")
#> To cite rwavelet in publications use:
#> 
#>   F. Navarro and C. Chesneau (2023). R package rwavelet: Wavelet
#>   Analysis (Version 0.4.1.99999). Available from
#>   https://github.com/fabnavarro/rwavelet
#> 
#> A BibTeX entry for LaTeX users is
#> 
#>   @Manual{,
#>     title = {R package {rwavelet}: Wavelet Analysis},
#>     author = {F. Navarro and C. Chesneau},
#>     year = {2023},
#>     note = {(Version 0.4.1.99999)},
#>     url = {https://github.com/fabnavarro/rwavelet},
#>   }