TITLE(wr @@ Discrete wavelet transform (reconstruction). )
This function performs the reconstruction stage of Mallat's pyramid algorithm
(Mallat 1989),
i.e. the discrete inverse wavelet transform. The actual transform is performed
by some C code, this is dynamically linked into S (if your machine can
do this).
USAGE(
wr(wd.object, start.level=0, verbose=F, return.object=F)
)
ARGUMENTS(
ARG(wd.object@@)
A wavelet decomposition object as returned by LANG(wd), and described in
the help for that function and the help for "wd.object".
ARG(start.level@@)
The level you wish to start reconstruction at. The is usually the first
(level 0).
ARG(verbose@@)
Controls the printing of "informative" messages whilst the computations
progress. Such messages are generally annoying so it is turned off by default.
ARG(return.object@@)
If this is F then the top level of the reconstruction is returned
(this is the reconstructed function at the highest resolution).
Otherwise if it is T the whole wd reconstructed object is returned.
)
PARA BOLD(VALUE)
Either a vector containing the top level reconstruction or
an object of class "wd" containing the results of the reconstruction,
details to be found in help for "wd.object".
PARA BOLD(SIDE EFFECTS)
The appropriate C object code is loaded if it isn't.
The code implements Mallat's pyramid algorithm (Mallat 1989).
In the reconstruction the quadrature mirror filters G and H are
supplied with c0 and d0, d1, ... d(m-1) (the wavelet coefficients)
and rebuild c1,..., cm.
If wd.object was obtained directly from wd then the original function
can be reconstructued EXACTLY as cm and can be sought with
> accessC(wd.object, level=wd.object\$levels)
Usually, the wd.object has been modified in some way, for example,
some coefficients set to zero by threshold. Wr then reconstructs
the function with that set of wavelet coefficients.
PARA BOLD(RELEASE)
Release 2.2
Copyright Guy Nason 1993
PARA BOLD(REFERENCES)
Any book on wavelets, especially
Chui, C. K. (1992)
An Introduction to Wavelets.
Academic Press, London.
Daubechies, I. (1988)
Orthonormal bases of compactly supported wavelets
Communications on Pure and Applied Mathematics, Vol. 41, 909-996
Mallat, S. G. (1989)
A theory for multiresolution signal decomposition: the wavelet representation
IEEE Transactions on Pattern Analysis and Machine Intelligence.
Vol. 11, Number 7 674-693.
PARA BOLD(SEE ALSO)
LANG(wd), LANG(accessC), LANG(accessD), LANG(filter.select), LANG(plot), LANG(dyn.load)
LANG(threshold)
BLANK

PARA BOLD( )
BLANK

EXAMPLES(
#
# Decompose and then exactly reconstruct test.data
#
> tdecomp <- wd(test.data)
> trecons <- wr(tdecomp)
> reconstructed <- accessC(trecons, level=trecons\$levels)
#
# Look at accuracy of reconstruction
> max(abs(reconstructed - test.data))
[1] 1.481482e-12
#
# Reconstruct a hard.thresholded object, look at the wavelet coefficients
#
> trecons <- wr(threshold(tdecomp, type="hard") )
> plot(trecons)
)
PARA ITALIC(File automatically converted from S(-PLUS) help format)
