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mwr

Multiple discrete wavelet transform (reconstruction).

DESCRIPTION

This function performs the reconstruction stage of Mallat's pyramid algorithm adapted for multiple wavelets (see Xia et al.(1996)), i.e. the discrete inverse multiple wavelet transform.

USAGE

mwr(mwd.object, prefilter.type = mwd$prefilter, verbose = F, start.level = 0,
	returnC = F)

REQUIRED ARGUMENTS

mwd.object: A multiple wavelet decomposition object as returned by mwd.

OPTIONAL ARGUMENTS

prefilter.type: Usually best not to change this (i.e. not to use a different prefilter on the reconstruction to the one used on decomposition).
verbose: Controls the printing of "informative" messages whilst the computations progress. Such messages are generally annoying so it is turned off by default.
start.level: The level you wish to start reconstruction at. The is usually the first (level 0).
returnC: If this is F then a vector of the same length as the argument data supplied to the function mwd that constructed the supplied mwd object. is returned, Ie. the reconstructed data. If true then the last level (highest resolution) C coefficients are returned in matrix form. This matrix has not been postprocessed.

VALUE

Either a vector containing the final reconstruction or a matrix containing unpostprocessed coefficients.

SIDE EFFECTS

None

DETAILS

The code implements Mallat's pyramid algorithm adapted for multiple wavelet decompositions (Xia et al. 1996). In the reconstruction the quadrature mirror filters G and H are supplied with C0 and D0, D1, ... D(J-1) (the wavelet coefficients) and rebuild C1,..., CJ.

The matrix CJ is postprocessed which returns the full reconstruction

If mwd.object was obtained directly from mwd then the original function can be reconstructued exactly. Usually, the mwd.object has been modified in some way, for example, some coefficients set to zero by threshold. Mwr then reconstructs the function with that set of wavelet coefficients.

RELEASE

EXAMPLES

#
# Decompose and then exactly reconstruct test.data
#
tdecomp <- mwd(test.data)
trecons <- mwr(tdecomp)
#
# Look at accuracy of reconstruction
 max(abs(tdrecons - test.data))
#[1] 2.266631e-12
#
# See also the example of using wr or mwr in
# the EXAMPLES section of
# the help for threshold.mwd.

mwr