wstCVl

Performs two-fold cross-validation estimation using packet-ordered non-decimated wavelet transforms and a (vector) level-dependent threshold.

DESCRIPTION

USAGE

wstCVl(ndata, ll = 3, type = "soft", filter.number = 10, family = 
	"DaubLeAsymm", tol = 0.01, verbose = 0, norm = 
	l2norm, InverseType = "average", uvdev = madmad)

REQUIRED ARGUMENTS

ndata

the noisy data. This is a vector containing the signal plus noise. The length of this vector should be a power of two.

OPTIONAL ARGUMENTS

ll

the primary resolution for this estimation. Note that the primary resolution is problem-specific: you have to find out which is the best value.

type

whether to use hard or soft thresholding. See the explanation for this argument in the threshold.wst function.

filter.number

This selects the smoothness of wavelet that you want to use in the decomposition. By default this is 10, the Daubechies least-asymmetric orthonormal compactly supported wavelet with 10 vanishing moments.

family

specifies the family of wavelets that you want to use. The options are "DaubExPhase" and "DaubLeAsymm".

tol

the cross-validation tolerance which decides when an estimate is sufficiently close to the truth (or estimated to be so).

verbose

If TRUE then informative messages are printed during the progression of the function, otherwise they are not.

norm

which measure of distance to judge the dissimilarity between the estimates. The functions l2norm and linfnorm are suitable examples.

InverseType

The possible options are "average" or "minent". The former uses basis averaging to form estimates of the unknown function. The "minent" function selects a basis using the Coifman and Wickerhauser, 1992 algorithm to select a basis to invert.

uvdev

Universal thresholding is used to generate an upper bound for the ideal threshold. This argument provides the function that computes an estimate of the variance of the noise for use with the universal threshold calculation (see threshold.wst).

VALUE

ndata

a copy of the input noisy data

xvwr

a reconstruction of the best estimate computed using this algorithm. It is the inverse (computed depending on what the InverseType argument was) of the xvwrWSTt component.

xvwrWSTt

a thresholded version of the packet-ordered non-decimated wavelet transform of the noisy data using the best threshold discovered by this cross-validation algorithm.

uvt

the universal threshold used as the upper bound for the algorithm that tries to discover the optimal cross-validation threshold. The lower bound is always zero.

xvthresh

the best threshold as discovered by cross-validation. Note that this is vector, a level-dependent threshold with one threshold value for each resolution level. The first entry corresponds to level ll, the last entry corresponds to level nlevels(ndata)-1 and the entries in between linearly to the levels in between. The wstCV function should be used to compute a global threshold.

optres

The results from performing the optimisation using the nlminb function from Splus. This object contains many interesting components with information about how the optimisation went. See the nlminb help page for information.

SIDE EFFECTS

DETAILS

Further, this function computes level-dependent thresholds. That is, it can compute a different threshold for each resolution level.

Note that the procedure outlined above can use AvBasis basis averaging or basis selection and inversion using the Coifman and Wickerhauser, 1992 best-basis algorithm

RELEASE

SEE ALSO

EXAMPLES

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