imwd: Two-dimensional wavelet transform (decomposition).

In LS2W: Locally Stationary Two-Dimensional Wavelet Process Estimation Scheme

Two-dimensional wavelet transform (decomposition).

Description

This function replaces WaveThresh's imwd which currently contains a minor bug (for the case type="station"_.The function can perform two types of two-dimensional discrete wavelet transform (DWT). The standard transform (type="wavelet") computes the 2D DWT according to Mallat's pyramidal algorithm (Mallat, 1989). The spatially ordered non-decimated 2D DWT (NDWT) (type="station") contains all possible spatially shifted versions of the DWT. The order of computation of the DWT is O(n), and it is O(n log n) for the NDWT if n is the number of pixels.

Usage

imwd(image, filter.number = 10, family = "DaubLeAsymm", type = "wavelet", 
bc = "periodic", RetFather = TRUE, verbose = FALSE)

Arguments

image	A square matrix containing the image data you wish to decompose. The sidelength of this matrix must be a power of 2.
filter.number	This selects the smoothness of wavelet that you want to use in the decomposition. By default this is 10, the Daubechies least-asymmetric orthonormal compactly supported wavelet with 10 vanishing moments.
family	Specifies the family of wavelets that you want to use. The options are "DaubExPhase" and "DaubLeAsymm".
type	Specifies the type of wavelet transform. This can be "wavelet" (default) in which case the standard 2D DWT is performed (as in previous releases of WaveThresh). If type is "station" then the 2D spatially-ordered non-decimated DWT is performed. At present, only periodic boundary conditions can be used with the 2D spatially ordered non-decimated wavelet transform.
bc	specifies the boundary handling. If bc=="periodic" the default, then the function you decompose is assumed to be periodic on it's interval of definition, if bc=="symmetric" then the function beyond its boundaries is assumed to be a symmetric reflection of the function in the boundary. The symmetric option was the implicit default in releases prior to 2.2. Note that only periodic boundary conditions are valid for the 2D spatially-ordered non-decimated wavelet transform.
RetFather	If TRUE then this argument causes the scaling function coefficients at each resolution level to be returned as well as the wavelet coefficients. If FALSE then no scaling function coefficients are returned. The opportunity of returning father wavelet coefficients has been added since previous versions of WaveThresh.
verbose	Controls the printing of "informative" messages whilst the computations progress. Such messages are generally annoying so it is turned off by default.

Value

An object of class imwd object containing the two-dimensional wavelet transform (possibly spatially-ordered non-decimated).

Author(s)

Idris Eckley and Guy Nason

References

Mallat, S.G. (1989b). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattn Anal. Mach. Intell., 11, 674-693.

See Also

cddews

Examples

#
#First let's create an image
#
tmp <- HaarMontage(direction="diagonal")
#
# Now let's do the 2D discrete wavelet transform on the image.
#
lwd <- imwd(tmp)
#
# Let's look at the coefficients
#
plot(lwd)

LS2W documentation built on Nov. 2, 2022, 1:06 a.m.