Wavelet Toolbox    

Penalized threshold for wavelet packet de-noising



THR = wpbmpen(T,SIGMA,ALPHA) returns a global threshold THR for de-noising. THR is obtained by a wavelet packet coefficients selection rule using a penalization method provided by Birge-Massart.

T is a wavelet packet tree corresponding to the wavelet packet decomposition of the signal or image to be de-noised.

SIGMA is the standard deviation of the zero mean Gaussian white noise in the de-noising model (see wnoisest for more information).

ALPHA is a tuning parameter for the penalty term. It must be a real number greater than 1. The sparsity of the wavelet packet representation of the de-noised signal or image grows with ALPHA. Typically ALPHA = 2.

THR minimizes the penalized criterion given by

let t* be the minimizer of

where c(k) are the wavelet packet coefficients sorted in decreasing order of their absolute value and n is the number of coefficients, then THR = c(t*).

wpbmpen(T,SIGMA,ALPHA,ARG) computes the global threshold and, in addition, plots three curves:


See Also
wbmpen, wden, wdencmp, wpdencmp

  wp2wtree wpcoef