treethresh (version 0.1-11)

wavelet.treethresh: Threshold wavelet coefficients

Description

wavelet.threshold is a more user-friendly function for thresholding wavelet coefficients stored in an wd or imwd object. It combines the functions extract.coefficients, estimate.sdev (rescales the coefficients accordingly), treethresh or wtthresh, prune, thresh, and insert.coefficients

Usage

wavelet.treethresh(object, sdev=NA, dev=mad, start.level=5,
                   levelwise=FALSE, v=5, sd.mult=0.5, postmed=TRUE, ...)

Arguments

object

An object of the class wd or wtthresh to be smoothed by thresholding.

sdev

The standard error of the noise (if known), otherwise NA.

dev

The function used to estimate the standard error. Typical examples are sd (teh default), or the more robust mad. Not used if sdev is given.

start.level

The level in the wavelet transform from which to commence thresholding the wavelet coefficients. This level and all those finer levels will be thresholded.

levelwise

Indicates whether the thresholding should be carried out independently for each level and type of coefficients as in the function treethresh (if levelwise=TRUE), or whether a common partition is to be found jointly for all coefficients as in the function wtthresh (if levelwise=FALSE).

v

The number of folds in the cross-validation used to determine the optimal subtree in the pruning step (see the function prune for details). NA if no pruning is to be carried out.

sd.mult

The smallest subtree that is not sd.mult times the standard error worse than the best loglikelihood will be chosen as the optimal tree in the pruning step. (see the function prune for details).

postmed

Controls whether thresholding is to be carried out by using the posterior median of the coefficient \(\mu|y\) (postmed=true) or by using a hard threshold (postmed=FALSE). (See the function thresh for more details.)

...

arguments passed to to wtthresh (if levelwise=FALSE) or treethresh (if levelwise=TRUE).

Value

Returns an object of the class wd or wtthresh, where the coefficients have been thresholded using the TreeThresh algorithm.

See Also

extract.coefficients, estimate.sdev, treethresh, wtthresh, prune, thresh, insert.coefficients

Examples

## The following examples shows how an example image can be
## thresholded step by step. All the steps are combined in the more
## user-friendly function wavelet.treethresh

## (01) Load the example image
data(tiles)

## (02) Display the image
par(mai=rep(0,4)) ; image(tiles,col=grey(0:255/255))

## (03) Add noise to the image
corrupted <- tiles + rnorm(length(tiles))

## (04) Display the corrupted image
par(mai=rep(0,4)) ; image(corrupted,col=grey(0:255/255))

## (05) Compute the wavelet transform
corrupted.wt <- imwd(corrupted)

## (06) Perform the thresholding
denoised.wt <- wavelet.treethresh(corrupted.wt)

## (07) Compute inverse wavelet transform
denoised <- imwr(denoised.wt)

## (08) Display denoised image
par(mai=rep(0,4)) ; image(denoised,col=grey(0:255/255))

## (09) Compute l2 loss
sum((denoised-tiles)^2)

## The call to wavelet.treethresh is equivalent to steps (06) to (13)
## of the example in the help section "coefficients".