WaveD {waved} | R Documentation |
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")
yobs |
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. |
MC |
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. |
SOFT |
if SOFT=TRUE, uses the soft thresholding policy as opposed to the hard (SOFT=FALSE, the default). |
F |
Finest resolution level; the default is the data-driven choice j1 (see Value below). |
L |
Lowest resolution level; the default is 3. |
deg |
The degree of the Meyer wavelet, either 1, 2, or 3 (the default). |
eta |
Tuning parameter of the maxiset threshold; default is $sqrt(6)$. |
thr |
A vector of length $F-L+1$, giving thresholds at each resolution levels L,L+1,...,F; default is maxiset threshold. |
label |
Auxiliary plotting parameter; do not change this. |
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
waved |
translation invariant WaveD transform; in the case MC=TRUE this is all that is returned. |
ordinary |
ordinary WaveD transform |
FWaveD |
Forward WaveD Transform; see FWaveD . |
w |
alternate name for FWaveD |
w.thr |
thresholded version of w |
IWaveD |
Inverse WaveD Transform |
iw |
alternate name for IWaveD |
s |
estimate of the noise standard deviation |
j1 |
estimate of optimal resolution level (for maxiset threshold). |
F |
Fine resolution level used (may be different to j1). |
M |
estimate of optimal Fourier frequency (for maxiset threshold). |
thr |
vector of thresholds used (default is maxiset threshold). |
percent |
percentage of thresholding per resolution level |
noise |
noise proxy, wavelet coefficients of the raw data at the largest resolution level, used for estimating noise features. |
ps |
P-value of the Shapiro-Wilk test for normality applied to the noise proxy. |
residuals |
wavelet coefficients that have been removed before fine level F. |
Marc Raimondo and Michael Stewart
Cavalier, L. and Raimondo, M. (2007), `Wavelet deconvolution with noisy eigen-values', {em IEEE Trans. Signal Process}, Vol. 55(6), In the press.
Donoho, D. and Raimondo, M. (2004), `Translation invariant deconvolution in a periodic setting', {em The International Journal of Wavelets, Multiresolution and Information Processing} {bf 14}(1),~415–423.
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. (2007), `The WaveD Transform in R', Journal of Statistical Software.
library(waved) data=waved.example(TRUE,FALSE) doppler.wvd=WaveD(data$doppler.noisy,data$g) summary(doppler.wvd)