WaveThresh
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GetRSSWST
Computes estimate of error for function estimate.
DESCRIPTION
Computes estimate of error for function estimate. Given noisy data and
a threshold value this function uses
Nason's 1996 two-fold cross-validation
algorithm, but using packet ordered non-decimated
wavelet transforms to compute two estimates of an underlying
``true'' function and uses them to compute an estimate of the
error in estimating the truth.
USAGE
GetRSSWST(ndata, threshold, levels, family = "DaubLeAsymm",
filter.number = 10, type = "soft", norm = l2norm, verbose = 0,
InverseType = "average")
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.
- threshold
- the value of the threshold that you wish to compute the error of the
estimate at
- levels
- the levels over which you wish the threshold value to be computed
(the threshold that is used in computing the estimate and error in the
estimate).
See the explanation for this argument in the
threshold.wst function.
OPTIONAL ARGUMENTS
- family
- specifies the family of wavelets that you want to use.
The options are "DaubExPhase" and "DaubLeAsymm".
- 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.
- type
- whether to use hard or soft thresholding.
See the explanation for this argument in the
threshold.wst function.
- norm
- which measure of distance to judge the dissimilarity between the
estimates. The functions l2norm and
linfnorm are suitable examples.
- verbose
- If
TRUE then informative messages are printed during the
progression of the function, otherwise they are not.
- 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.
VALUE
A real number which is estimate of the error between estimate and truth
at the given threshold.
SIDE EFFECTS
None.
DETAILS
This function implements the component of
the cross-validation method detailed by
Nason, 1996
for computing an estimate of the error between an estimate and the
``truth''.
The difference here is that it uses the
packet ordered non-decimated wavelet transform
rather than the standard Mallat wd discrete wavelet
transform. As such it is an example of
the translation-invariant denoising of
Coifman and Donoho, 1995 but uses
cross-validation to choose the threshold rather than SUREshrink.
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
Version 3.6 Copyright Guy Nason 1995
SEE ALSO
linfnorm,
linfnorm,
wstCV,
wstCVl.
EXAMPLES
#
# This function performs the error estimation step for the
# wstCV function and so is not intended for
# user use.
#