WaveThresh Help - imwd

imwd

Discrete wavelet transform for images (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, family="DaubExPhase", bc="periodic", verbose=F)

REQUIRED 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.

OPTIONAL ARGUMENTS

filter.number: The filter that you wish to use to decompose the function. The filters are obtained from the filter.select function.
family: The type of wavelet family that you wish to use. The filter families that you can use are described in the help to the filter.select function.
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 decomposition to act as if the function extended by symmetric reflection at each end.
verbose: If this argument is true then informative messages are printed whilst the computations are performed.

VALUE

An object of class imwd, a list containing the wavelet coefficients.

SIDE EFFECTS

Unfortunately not.

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.

RELEASE

REFERENCES

Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 11, 674--693.

Nason, G. P. and Silverman, B. W. (1994). The discrete wavelet transform in S. Journal of Computational and Graphical Statistics, 3, 163--191.

EXAMPLES

#
# Do a decomposition of an image
#
tdecomp <- imwd(test.image)
#
# Look at the coefficients by plotting the result
#
plot(tdecomp)

Wavelets Home Page

G.P.Nason@bristol.ac.uk