wdcbm2
Thresholds for wavelet 2-D using Birgé-Massart strategy
Syntax
[THR,NKEEP] = wdcbm2(C,S,ALPHA,M)
wdcbm2(C,S,ALPHA)
wdcbm2(C,S,ALPHA,prod(S(1,:)))
Description
[THR,NKEEP] = wdcbm2(C,S,ALPHA,M) returns
level-dependent thresholds THR and numbers of coefficients
to be kept NKEEP, for de-noising or compression. THR is
obtained using a wavelet coefficients selection rule based on the
Birgé-Massart strategy.
[C,S] is the wavelet decomposition structure
of the image to be de-noised or compressed, at level j =
size(S,1)-2.
ALPHA and M must be real
numbers greater than 1.
THR is a matrix 3 by j; THR(:,i) contains
the level dependent thresholds in the three orientations: horizontal,
diagonal, and vertical, 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 de-noising.
A default value for M is M = prod(S(1,:)),
the length of the coarsest approximation coefficients, since the previous
formula leads for i = j+1, to nj+1 = M = prod(S(1,:)).
Recommended values for M are from prod(S(1,:)) to 6*prod(S(1,:)).
wdcbm2(C,S,ALPHA) is equivalent to wdcbm2(C,S,ALPHA,prod(S(1,:))).
Examples
% Load original image.
load detfingr;
nbc = size(map,1);
% Perform a wavelet decomposition of the image
% at level 3 using sym4.
wname = 'sym4'; lev = 3;
[c,s] = wavedec2(X,lev,wname);
% Use wdcbm2 for selecting level dependent thresholds
% for image compression using the adviced parameters.
alpha = 1.5; m = 2.7*prod(s(1,:));
[thr,nkeep] = wdcbm2(c,s,alpha,m)
thr =
21.4814 46.8354 40.7907
21.4814 46.8354 40.7907
21.4814 46.8354 40.7907
nkeep =
624 961 1765
% Use wdencmp for compressing the image using the above
% thresholds with hard thresholding.
[xd,cxd,sxd,perf0,perfl2] = ...
wdencmp('lvd',c,s,wname,lev,thr,'h');
% Plot original and compressed images.
colormap(pink(nbc));
subplot(221), image(wcodemat(X,nbc)),
title('Original image')
subplot(222), image(wcodemat(xd,nbc)),
title('Compressed image')
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.