Penalized threshold for wavelet 1-D or 2-D de-noising.
THR = wbmpen(C,L,SIGMA,ALPHA) wbmpen(C,L,SIGMA,ALPHA,ARG)
global threshold. THR is obtained by a wavelet coefficients selection rule using a penalization method provided by Birge-Massart.
is the wavelet decomposition structure of the signal or image to be de-noised.
is the standard deviation of the zero mean Gaussian white noise in the de-noising model (see WNOISEST for more information).
is a tuning parameter for the penalty term and it must be a real number greater than 1. The sparsity of the wavelet representation of the de-noised signal or image grows with ALPHA. Typically ALPHA = 2.
do some plotting
THR minimizes the penalized criterion given by: let t* be the minimizer of crit(t) = -sum(c(k)^2,k<=t) + 2*SIGMA^2*t*(ALPHA + log(n/t)) where c(k) are the wavelet coefficients sorted in decreasing order of their absolute value and n is the number of coefficients; then THR = |c(t*)|.