wavelet.treethresh: Threshold wavelet coefficients
In treethresh: Methods for Tree-Based Local Adaptive Thresholding

Description Usage Arguments Value Note See Also Examples

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

1 2	wavelet.treethresh(object, sdev=NA, dev=mad, start.level=5, levelwise=FALSE, v=5, sd.mult=0.5, postmed=TRUE, ...)

`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`).

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

wavelet.treethresh combines the functions extract.coefficients, estimate.sdev (and the appropriate scaling), treethresh / wtthresh, prune, insert.coefficients into a single (hopefully) more user-friendly function.

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

## 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".