wavethresh (version 4.6.1)

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:
• 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

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.

See Also

imwd,tpwr

Examples

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