# wbmpen

Penalized threshold for wavelet 1-D or 2-D denoising

## Description

returns the global threshold `thr`

= wbmpen(`c,l`

,`sigma`

,`alpha`

)`thr`

for denoising.
`c,l`

is the wavelet decomposition structure of the signal or
image to be denoised. `sigma`

is the standard deviation of the
zero mean Gaussian white noise in the denoising model (see `wnoisest`

for more information).
`alpha`

is a tuning parameter for the penalty term.

computes the global threshold and plots three curves:`thr`

= wbmpen(`c,l`

,`sigma`

,`alpha`

,ARG)

`2×sigma^2×t×(alpha + log(n/t))`

`sum(c(k)^2,k≤t)`

`crit(t)`

where `n`

is the number of coefficients and

crit(t) = -sum(c(k)^2,k≤t) + 2×sigma^2×t×(alpha + log(n/t)).

## Examples

## Input Arguments

## Output Arguments

## More About

## References

[1] Birgé, Lucien, and Pascal
Massart. “From Model Selection to Adaptive Estimation.” In *Festschrift for
Lucien Le Cam*, edited by David Pollard, Erik Torgersen, and Grace L.
Yang, 55–87. New York, NY: Springer New York, 1997.
https://doi.org/10.1007/978-1-4612-1880-7_4.

## Version History

**Introduced before R2006a**