WaveThresh Help

threshold.mwd

Use threshold on an mwd object.

DESCRIPTION

Applies hard or soft thresholding to multiple wavelet decomposition object mwd.object.

USAGE

threshold.mwd(mwd, levels = 3:(mwd$nlevels - 1), type = "hard",
	policy = "universal", boundary = F, verbose = F, return.threshold = F,
	threshold = 0, covtol = 1e-09, robust = T, return.chisq = F,
	bivariate = T)

REQUIRED ARGUMENTS

mwd: The multiple wavelet decomposition object that you wish to threshold.

OPTIONAL ARGUMENTS

levels: a vector of integers which determines which scale levels are thresholded in the decomposition. Each integer in the vector must refer to a valid level in the mwd object supplied. This is usually any integer from 0 to nlevels(wd)-1 inclusive. Only the levels in this vector contribute to the computation of the threshold and its application.
type: determines the type of thresholding this can be "hard" or "soft".
policy: selects the technique by which the threshold value is selected. Each policy corresponds to a method in the literature. At present the different policies are "universal", "manual", "single". The policies are described in detail below.
boundary: If this argument is TRUE then the boundary bookeeping values are included for thresholding, otherwise they are not.
verbose: if TRUE then the function prints out informative messages as it progresses.
return.threshold: If this option is TRUE then the actual value of the threshold is returned. If this option is FALSE then a thresholded version of the input is returned.
threshold: This argument conveys the user supplied threshold. If the policy="manual" then value is the actual threshold value. Any other policy means that the threshold value is ignored.
covtol: The tolerance for what constitutes a singular variance matrix. If smallest eigenvalue of the estimated variance matrix is less than covtol then it is assumed to be singular and no thresholing is done at that level. Note: do not confuse covtol with cvtol an argument in threshold.wd.
robust: If true the variance matrix at each level is estimated using a robust method (mad) otherwise it is estimated using var().
return.chisq: If true the vector of values to be thresholded is returned. These values are a quadratic form of each coefficient vector, and under normal assumptions the noise component will have a chi-squared distribution (see Downie and Silverman 1996).

VALUE

An object of class mwd. This object contains the thresholded wavelet coefficients. Note that if the return.threshold option is set to TRUE then the threshold values will be returned, or if return.chisq the vector of values to be thresholded will be returned, rather than the thresholded object.

SIDE EFFECTS

None

DETAILS

Thresholding modifies the coefficients within a mwd object. The modification can be performed either with a "hard" or "soft" thresholding selected by the type argument.

Unless policy="single", the following method is applied. The columns of mwd$D are taken as coefficient vectors D_j,k. From these chisq_j,k=D_j,k . V_j^-1 . D_j,k is computed, where V_j^-1 is the inverse of the estimated variance of the coefficient vectors in that level (j). Chisq_j,k is a positive scalar which is to be thresholded in a similar manner to univariate hard or soft thresholding. To obtain the new values of D_j,k shrink the vector by the same proportion as was the corresponding chisq_j,k term.

POLICIES

single: If policy="single" then univariate thresholding is applied to each element of D as in (Strela et al 1999).
universal: The universal threshold is computed using 2log(n) (See Downie & Silverman 1996) where n is the number of coefficient vectors to be thresholded.
manual: The "manual" policy is simple. You supply a threshold value to the threshold argument and hard or soft thresholding is performed using that value.

EXAMPLES

#
# Generate some test data
#
test.data <- example.1()$y 
tsplot(test.data)

#
# Generate some noisy data
#
ynoise <- test.data + rnorm(512, sd=0.1)
#
# Plot it
#
tsplot(ynoise)

#
# Now take the discrete multiple wavelet transform
# N.b. I have no idea if the default wavelets here are appropriate for
# this particular example. 
#
ynmwd <- mwd(ynoise)
plot(ynwd)

# [1] 2.020681 2.020681 2.020681 2.020681 2.020681 2.020681 2.020681
#
# Now do thresholding. We'll use the default arguments.
#
ynmwdT <- threshold(ynmwd)
#
# And let's plot it
#
plot(ynmwdT)

#
# Let us now see what the actual estimate looks like
#
ymwr <- wr(ynwdT)
#
# Here's the estimate... 
#
tsplot(ywr1)