R: Multiple discrete wavelet transform (reconstruction).

mwr {wavethresh} | R Documentation

## 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, prefilter.type = mwd$prefilter, verbose = FALSE, start.level = 0,
    	returnC = FALSE)

### Arguments

`mwd` | A multiple wavelet decomposition object as returned by `mwd`.
`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 FALSE 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.

### 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 examples, some coefficients set to zero by `threshold`. Mwr then reconstructs the function with that set of wavelet coefficients.

See also Downie and Silverman, 1998

### Value

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

### RELEASE

Version 3.9.6 (Although Copyright Tim Downie 1996)

### Author(s)

Tim Downie

### See Also

`accessC.mwd`, `accessD.mwd`, `draw.mwd`, `mfirst.last`, `mfilter.select`, `mwd`, `mwd.object`, `plot.mwd`, `print.mwd`, `putC.mwd`, `putD.mwd`, `summary.mwd`, `threshold.mwd`, `wd`, `wr.mwd`.

### Examples

    #
    # Decompose and then exactly reconstruct test.data
    #
    test.data <- rnorm(128)
    tdecomp <- mwd(test.data)
    trecons <- mwr(tdecomp)
    #
    # Look at accuracy of reconstruction
    max(abs(trecons - test.data))
    #[1] 2.266631e-12
    #
    # See also the examples of using \code{\link{wr}} or mwr in
    # the \code{examples} section of
    # the help for \code{\link{threshold.mwd}}.

[Package wavethresh version 4.6.8 Index]