denoiseheteroprop {adlift}R Documentation

denoiseheteroprop

Description

Denoises the inputted signal using artificial levels noise variance estimation and bayesian thresholding, assuming noise variances known up to proportionality constants.

Usage

denoiseheteroprop(x, f, pred, neigh, int, clo, keep, rule = "median",gamvec)

Arguments

x A vector of grid values. Can be of any length, not necessarily equally spaced.
f A vector of function values corresponding to x. Must be of the same length as x.
pred The type of regression to be performed. Possible options are LinearPred, QuadPred, CubicPred, AdaptPred and AdaptNeigh.
neigh The number of neighbours over which the regression is performed at each step. If clo is false, then this in fact denotes the number of neighbours on each side of the removed point.
int Indicates whether or not the regression curve includes an intercept.
clo Refers to the configuration of the chosen neighbours. If clo is false, the neighbours will be chosen symmetrically around the removed point. Otherwise, the closest neighbours will be chosen.
keep The number of scaling coefficients to be kept in the final representation of the initial signal. This must be at least two.
rule The type of bayesian thresholding used in the procedure. Possible values are "mean", "median" (posterior mean or median thresholding) or "hard or "soft" (hard or soft thresholding).
gamvec a vector of proportions of the noise standard deviations (in the order of x).

Details

The function uses the transform matrix to normalise the detail coefficients produced from the forward transform, so that they can be used in the bayesian thresholding procedure EbayesThresh. The normalising factors are calculated assuming that the noise associated to the ith gridpoint is gamma_{i}σ. The coefficients are divided into artificial levels, and the first (largest)level is used to estimate the noise variance of the coefficients. EbayesThresh is then used to threshold the coefficients. The resulting new coefficients are then unnormalised and the transform inverted to obtain an estimate of the true (unnoisy) signal.

Value

out the output from the forward transform.
w the matrix associated to the wavelet transform.
indsd the individual coefficient variances introduced by the transform.
al the artificial levels used to estimate the noise variance.
sd the standard deviation of the noise.
fhat the estimate of the function after denoising.

Author(s)

Matt Nunes (matt.nunes@bristol.ac.uk), Marina Popa (Marina.Popa@bristol.ac.uk)

See Also

denoise

Examples

x1<-runif(256)
y1<-make.signal2("doppler",x=x1)
n1<-rnorm(256,0,.1)
z1<-y1+n1
gvec<-c(rep(.4,times=100),rep(.7,times=100),rep(.3,times=56))
#
est1<-denoiseheteroprop(x1,z1,AdaptNeigh,1,TRUE,TRUE,2,"median",gvec)
sum(abs(y1-est1$fhat$coeff))
#
#the error between the true signal and the denoised version. 


[Package adlift version 0.9-6 Index]