tpwd: Tensor product 2D wavelet transform

Description

Performs the tensor product 2D wavelet transform. This is a related, but different, 2D wavelet transform compared to imwd.

Usage

tpwd(image, filter.number = 10, family = "DaubLeAsymm", verbose = FALSE)

Value

A list with the following components:

tpwd: A matrix with the same dimensions as the input image, but containing the tensor product wavelet transform coefficients.
filter.number: The filter number used
family: The wavelet family used
type: The type of transform used
bc: The boundary conditions used
date: When the transform occurred

Arguments

image: The image you wish to subject to the tensor product WT
filter.number: The smoothness of wavelet, see filter.select
family: The wavelet family you wish to use
verbose: Whether or not you wish to print out informative messages

Author

G P Nason

Details

The transform works by first taking the regular 1D wavelet transform across all columns in the image and storing these coefficients line by line back into the image. Then to this new image we apply the regular 1D wavelet transform across all rows in the image.

Hence, the top-left coefficient is the smoothed version both horizontally and vertically. The left-most row contains the image smoothed horiztonally, but then detail picked up amongst the horizontal smooths vertically.

Suggested by Rainer von Sachs.

Examples

Run this code

data(lennon)
ltpwd <- tpwd(lennon)
if (FALSE) image(log(abs(ltpwd$tpwd)), col=grey(seq(from=0, to=1, length=100)))

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