wdcbm
Thresholds for wavelet 1-D using Birgé-Massart strategy
Syntax
[THR,NKEEP] = wdcbm(C,L,ALPHA,M)
wdcbm(C,L,ALPHA)
wdcbm(C,L,ALPHA,L(1))
Description
[THR,NKEEP] = wdcbm(C,L,ALPHA,M) returns level-dependent thresholds
THR and numbers of coefficients to be kept NKEEP,
for denoising or compression. THR is obtained using a wavelet
coefficients selection rule based on the Birgé-Massart strategy.
[C,L] is the wavelet decomposition structure of the signal to be denoised
or compressed, at level j = length(L)-2. ALPHA and
M must be real numbers greater than 1.
THR is a vector of length j; THR(i) contains
the threshold for level i.
NKEEP is a vector of length j; NKEEP(i) contains
the number of coefficients to be kept at level i.
j, M and ALPHA define
the strategy:
At level j+1 (and coarser levels), everything is kept.
For level i from 1 to j, the ni largest coefficients are kept with ni =
M/ (j+2-i)ALPHA.
Typically ALPHA = 1.5 for compression and ALPHA = 3 for
denoising.
A default value for M is M = L(1),
the number of the coarsest approximation coefficients, since the previous
formula leads for i = j+1, to nj+1 = M = L(1).
Recommended values for M are from L(1)
to 2*L(1).
wdcbm(C,L,ALPHA) is equivalent to wdcbm(C,L,ALPHA,L(1)).
Examples
% Load electrical signal and select a part of it.
load leleccum; indx = 2600:3100;
x = leleccum(indx);
% Perform a wavelet decomposition of the signal
% at level 5 using db3.
wname = 'db3'; lev = 5;
[c,l] = wavedec(x,lev,wname);
% Use wdcbm for selecting level dependent thresholds
% for signal compression using the adviced parameters.
alpha = 1.5; m = l(1);
[thr,nkeep] = wdcbm(c,l,alpha,m)
thr =
19.5569 17.1415 20.2599 42.8959 15.0049
nkeep =
1 2 3 4 7
% Use wdencmp for compressing the signal using the above
% thresholds with hard thresholding.
[xd,cxd,lxd,perf0,perfl2] = ...
wdencmp('lvd',c,l,wname,lev,thr,'h');
% Plot original and compressed signals.
subplot(211), plot(indx,x), title('Original signal');
subplot(212), plot(indx,xd), title('Compressed signal');
xlab1 = ['2-norm rec.: ',num2str(perfl2)];
xlab2 = [' % -- zero cfs: ',num2str(perf0), ' %'];
xlabel([xlab1 xlab2]);
References
Birgé, L.; P. Massart (1997), “From model selection to adaptive estimation,” in D. Pollard (ed), Festchrift for L. Le Cam, Springer, pp. 55–88.