waved (version 1.3)

FWaveD: 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)

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 \(C=L\).

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 \(L,L+1,\ldots,F\); default is maxiset threshold.

SOFT

if SOFT=TRUE, uses the soft thresholding policy as opposed to the hard (SOFT=FALSE, the default).

References

Johnstone, I., Kerkyacharian, G., Picard, D. and Raimondo, M. (2004), `Wavelet deconvolution in a periodic setting', Journal of the Royal Statistical Society, Series B 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)