FWaveD {waved}R Documentation

FWaveD

Description

Computes the Forward WaveD Transform.

Usage

FWaveD(y, g = 1, L = 3, deg = 3, F = (log2(length(y)) - 1), thr = rep(0, log2(length(y))), SOFT = FALSE)

Arguments

y Sample of $f*g$ + (Gaussian noise), a vector of dyadic length (i.e. $2^(J-1)$ where J is the largest resolution level). Here f is the target function, g is the convolution kernel.
g Sample of g or g + (Gaussian noise), same length as yobs. The default is the Dirac mass at 0.
L Lowest resolution level; the default is 3.
deg The degree of the Meyer wavelet, either 1, 2, or 3 (the default).
F Finest resolution level; the default is the data-driven choice j1 (see Value below).
thr A vector of length $F-L+1$, giving thresholds at each resolution levels L,L+1,...,F; default is maxiset threshold.
SOFT if SOFT=TRUE, uses the soft thresholding policy as opposed to the hard (SOFT=FALSE, the default).

Value

Returns a vector of wavelet coefficients of length n (the same length as y), the last n/2 entries are wavelet coefficients at resolution level $J-1$, where $J = log_2(n)$; the $n/4$ entries before that are the wavelet coefficients at resolution level $J-2$, and so on until level L. In addition the $2^L$ entries are scaling coefficients at coarse level C=L.

References

Johnstone, I., Kerkyacharian, G., Picard, D. and Raimondo, M. (2004), `Wavelet deconvolution in a periodic setting', {em Journal of the Royal Statistical Society, Series B} {bf 66}(3),~547–573. with discussion pp.627-652.

Raimondo, M. and Stewart, M. (2006), `The WaveD Transform in R', preprint, School and Mathematics and Statistics, University of Sydney.

See Also

WaveD

Examples

library(waved)
data=waved.example(TRUE,FALSE)
lidar.w=FWaveD(data$lidar.blur,data$g)

[Package waved version 1.0 Index]