R: Inverse two-dimensional discrete wavelet transform.

imwr.imwd {wavethresh} | R Documentation

## Inverse two-dimensional discrete wavelet transform.

### Description

This functions performs the reconstruction stage of Mallat's pyramid algorithm (i.e. the inverse discrete wavelet transform) for images.

### Usage

    ## S3 method for class 'imwd'
    imwr(imwd, bc=imwd$bc, verbose=FALSE, ...)

### Arguments

`imwd` | An object of class '`imwd`'. This type of object is returned by '`imwd`'.
`bc` | This argument specifies the boundary handling, it is best left to be the boundary handling specified by that in the supplied imwd (as is the default).
`verbose` | If this argument is true then informative messages are printed detailing the computations to be performed
`...` | any other arguments

### Details

Details of the algorithm are to be found in Mallat (1989). Similarly to the decomposition function, `imwd` the inverse algorithm works by applying many 1D reconstruction algorithms to the coefficients. The filters in these 1D reconstructions are incorporated in the supplied `imwd.object` and originally created by the `filter.select` function in WaveThresh3.

This function is a method for the generic function `imwr` for class `imwd.object`. It can be invoked by calling `imwr` for an object of the appropriate class, or directly by calling imwr.imwd regardless of the class of the object.

### Value

A matrix, of dimension determined by the original data set supplied to the initial decomposition (more precisely, determined by the `nlevelsWT` component of the `imwd.object`). This matrix is the highest resolution level of the reconstruction. If a `imwd` two-dimensional wavelet transform is followed immediately by a `imwr` inverse two-dimensional wavelet transform then the returned matrix will be exactly the same as the original image.

### RELEASE

Version 3.5.3 Copyright Guy Nason 1994

### Author(s)

G P Nason

### See Also

`imwd`, `imwd.object`, `imwr`.

### Examples

    #
    # Do a decomposition, then exact reconstruction
    # Look at the error
    #
    test.image <- matrix(rnorm(32*32), nrow=32)
    #
    # Test image is just some sort of  square matrix whose side length
    # is a power of two.
    #
    max( abs(imwr(imwd(test.image)) - test.image))
    # [1] 1.014611e-11

[Package wavethresh version 4.6.8 Index]