Performs statistical wavelet deconvolution using Meyer wavelet.
WaveD(yobs,g=c(1,rep(0,(length(yobs)-1))),MC=FALSE,SOFT=FALSE,
F=find.j1(g,scale(yobs))[2],L=3,deg=3,eta=sqrt(6),
thr=maxithresh(yobs,g,eta=eta),label="WaveD")In the case that MC=TRUE, WaveD returns a vector consisting of the translation-invariant WaveD estimate. In the case that MC=FALSE (the default), WaveD returns a list with components
translation invariant WaveD transform; in the case MC=TRUE this is all that is returned.
ordinary WaveD transform
Forward WaveD Transform; see FWaveD.
alternate name for FWaveD
thresholded version of w
Inverse WaveD Transform
alternate name for IWaveD
estimate of the noise standard deviation
estimate of optimal resolution level (for maxiset threshold).
Fine resolution level used (may be different to j1).
estimate of optimal Fourier frequency (for maxiset threshold).
vector of thresholds used (default is maxiset threshold).
percentage of thresholding per resolution level
noise proxy, wavelet coefficients of the raw data at the largest resolution level, used for estimating noise features.
P-value of the Shapiro-Wilk test for normality applied to the noise proxy.
wavelet coefficients that have been removed before fine level F.
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.
Sample of \(g\) or \(g\) + (Gaussian noise), same length as yobs. The default is the Dirac mass at 0.
Option to only return the (fast) translation-invariant WaveD estimate (MC=TRUE) as opposed to the full WaveD output (MC=FALSE, the default), as described below. MC=TRUE recommended for Monte Carlo simulation.
if SOFT=TRUE, uses the soft thresholding policy as opposed to the hard (SOFT=FALSE, the default).
Finest resolution level; the default is the data-driven choice j1 (see Value below).
Lowest resolution level; the default is 3.
The degree of the Meyer wavelet, either 1, 2, or 3 (the default).
Tuning parameter of the maxiset threshold; default is \(\sqrt6\).
A vector of length \(F-L+1\), giving thresholds at each resolution levels \(L,L+1,\ldots,F\); default is maxiset threshold.
Auxiliary plotting parameter; do not change this.
Marc Raimondo and Michael Stewart
Cavalier, L. and Raimondo, M. (2007), `Wavelet deconvolution with noisy eigen-values', IEEE Trans. Signal Process, Vol. 55(6), In the press.
Donoho, D. and Raimondo, M. (2004), `Translation invariant deconvolution in a periodic setting', The International Journal of Wavelets, Multiresolution and Information Processing 14(1),415--423.
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. (2007), `The WaveD Transform in R', Journal of Statistical Software.
FWaveD
library(waved)
data=waved.example(TRUE,FALSE)
doppler.wvd=WaveD(data$doppler.noisy,data$g)
summary(doppler.wvd)
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