wavethresh (version 2.2-6)

imwd: 2D Discrete Wavelet Transform (Image W. Decomposition)

Description

This function performs the decomposition stage of Mallat's pyramid algorithm i.e. the discrete wavelet transform for images.

Usage

imwd(image, filter.number=2, bc="periodic", verbose=FALSE)

Arguments

image

Square matrix containing the image. The number of rows in the image must be a power of 2. Since the matrix is square, this is also the number of columns in the matrix.

filter.number

The filter that you wish to use to decompose the function. The filters are obtained from the "filter.select" function and are the compactly supported orthonormal wavelets as described in Daubechies, I.

bc

boundary treatment. The periodic (default) treatment causes the decomposition to act as if the function you are trying to decompose is periodic (on it's own interval). The other option is symmetric, which used to be the default. This causes the decomposit

verbose

logical; if true then informative messages are printed whilst the computations are performed.

Value

• An object of class "imwd", a list containing the wavelet coefficients (see "imwd.object").

Details

The 2D algorithm is essentially the application of many 1D filters. First, the columns are attacked with the smoothing (H) and bandpass (G) filters, and the rows of each of these resultant images are attacked again with each of G and H, this results in 4 images. Three of them, GG, GH, and HG correspond to the highest resolution wavelet coefficients. The HH image is a smoothed version of the original and can be further attacked in exactly the same way as the original image to obtain GG(HH), GH(HH), and HG(HH), the wavelet coefficients at the second highest resolution level and HH(HH) the twice-smoothed image, which then goes on to be further attacked.

After each attack the dimension of the images is halved. After many attacks you will obtain four real numbers, one of which correspond to the image smoothed many times.

Exact details of the algorithm are to be found in Mallat 1989.

See Also

wd, for background information; imwr for reconstruction, plot.imwd, draw.imwd # Do a decomposition of an image # data(lennon) imwdL <- imwd(lennon) # Look at the coefficients --> example(plot.imwd) smooth nonlinear