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)

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

Value

A list with the following components:
tpwdA matrix with the same dimensions as the input image, but containing the tensor product wavelet transform coefficients.
filter.numberThe filter number used
familyThe wavelet family used
typeThe type of transform used
bcThe boundary conditions used
dateWhen the transform occurred

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)
image(log(abs(ltpwd$tpwd)), col=grey(seq(from=0, to=1, length=100)))

Run the code above in your browser using DataLab

Data Engineering and BI courses are free this week!