treethresh (version 0.1-11)

coefficients: Extracting and updating coefficients stored in wd or imwd objects

Description

extract.coefficients extracts wavelet coefficient vectors (in case of wd) and coefficient matrices (in case of imwd), so that these can be thresholded by treethresh or wtthresh. update.coefficients re-inserts these vector or matrices into the wd or imwd objects, such that the inverse transform can be computed using the thresholded coefficients.

Usage

# S3 method for wd
extract.coefficients(object, start.level=5)
# S3 method for wd
insert.coefficients(object, update)
# S3 method for imwd
extract.coefficients(object, start.level=5)
# S3 method for imwd
insert.coefficients(object, update)

Arguments

object

For extract.coefficients the wd or imwd object to extract the coefficients from. For insert.coefficients the wd or imwd object to be updated.

start.level

The coarsest level of coefficients to be extracted (extract.coefficients only)

update

A list with the matrices that should be copied into the wd or imwd object. (update.coefficients only)

...

additional arguments (see above for supported arguments).

Value

extract.coefficients returns the coefficient matrices to be extracted. update.coefficients returns the updated wd or imwd object.

insert.coefficients returns the updated wd or imwd object into which the coefficients from update have been inserted.

References

Evers, L. and Heaton T. (2009) Locally adaptive tree-based tresholding.

See Also

treethresh, wtthresh, wavelet.treethresh

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) Estimate the standard error
dev <- estimate.sdev(corrupted.wt)

## (07) Extract the coefficient matrices to be thresholded
coefs <- extract.coefficients(corrupted.wt)

## (08) Rescale the coefficients using the estimated standard error
## (should be around 1)
for (nm in names(coefs))
  coefs[[nm]] <- coefs[[nm]] / dev

## (09) Compute the tree
coefs.tree <- wtthresh(coefs)

## (10) Prune the tree
coefs.pruned.tree <- prune(coefs.tree)

## (11) Threshold according to the pruned tree
coefs.threshed <- thresh(coefs.pruned.tree)

## (12) Undo the rescaling
for (nm in names(coefs))
  coefs.threshed[[nm]] <- coefs.threshed[[nm]] * dev

## (13) Update coefficients
denoised.wt <- insert.coefficients(corrupted.wt, coefs.threshed)

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

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

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

## Equivalently we could have called
## denoised.wt <- wavelet.treethresh(corrupted.wt)
## instead of steps (06) - (13)