InvBasis.wst(wst, nv)
2^J = n where n is the number of
data points of the input vector. As such the packet-ordered
non-decimated wavelet transform contains a library of all possible shifted
wavelet bases.
Basis selection
It is possible to select a particular basis and invert the representation
with respect to the selected basis. This is what InvBasis.wst
does.
In WaveThresh such a basis is selected by creating a
nv (node.vector) class object which identifies
the basis. Then the function InvBasis takes
the wavelet representation and the node.vector and inverts the representation
with respect to the selected basis. The two functions
MaNoVe and numtonv
create a node.vector: the first by using a
Coifman-Wickerhauser
minimum entropy best-basis algorithm and the second by basis index.
Basis averaging. Rather than select a basis it is often useful to preserve information from all of the bases. For example, in curve estimation, after thresholding a wavelet representation the coefficients are coefficients of an estimate of the truth with respect to all of the shifted basis functions. Rather than select one of them we can average over all estimates. This sometimes gives a better curve estimate and can, for example, get rid of Gibbs effects. See Coifman and Donoho (1995) for more information on how to do curve estimation using the packet ordered non-decimated wavelet transform, thresholding and basis averaging.
For an example of denoising using the packet-ordered non-decimated wavelet transform and basis averaging see Johnstone and Silverman, 1997. The WaveThresh implementation of the basis averaging algorithm is to be found in Nason and Silverman, 1995
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# See example in the help to MaNoVe.wst
# for an example of InvBasis.wst
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