wpdencmp (Wavelet Toolbox)

De-noising or compression using wavelet packet.

[XD,TREED,DATAD,PERF0,PERFL2] = 
wpdencmp(X,SORH,N,'wname',CRIT,PAR,KEEPAPP)
[XD,TREED,DATAD,PERF0,PERFL2] = 
wpdencmp(TREE,DATA,SORH,CRIT,PAR,KEEPAPP)

Description

wpdencmp is a one- or two-dimensional de-noising and compression oriented function.

wpdencmp performs a de-noising or compression process of a signal or an image, using wavelet packet. The ideas and the procedures for de-noising and compression using wavelet packet are the same as those used in the wavelets framework (see wden and wdencmp).

[XD,TREED,DATAD,PERF0,PERFL2] = 
wpdencmp(X,SORH,N,

'wname',CRIT,PAR,KEEPAPP) returns a de-noised or compressed version XD of input signal X (one- or two-dimensional) obtained by wavelet packet coefficients thresholding.

Additional output arguments [TREED,DATAD] are the wavelet packet best decomposition structure (see besttree) of XD. PERFL2 and PERF0 are L² recovery and compression scores in percentages.

PERFL2 = 100 * (vector-norm of WP-cfs of XD / vector-norm of WP-cfs of X)².

If X is a one-dimensional signal and 'wname' an orthogonal wavelet, PERFL2 is

reduced to

SORH ('s' or 'h') is for soft or hard thresholding (see wthresh for more details).

Wavelet packet decomposition is performed at level N and 'wname' is a string containing wavelet name. Best decomposition is performed using entropy criterion defined by string CRIT and parameter PAR (see wentropy for details). Threshold parameter is also PAR. If KEEPAPP = 1, approximation coefficients cannot be thresholded, otherwise it is possible.

[XD,TREED,DATAD,PERF0,PERFL2] = 
wpdencmp(TREE,DATA,SORH,CRIT,PAR,KEEPAPP)

has the same output arguments, using the same options as above, but obtained directly from the input wavelet packet decomposition structure [TREE,DATA] (see maketree and wpdec) of the signal to be de-noised or compressed.

In addition if CRIT = 'nobest' no optimization is done and the current decomposition is thresholded.

Examples

% Load original signal. 
    load sumlichr; x = sumlichr;

% Use wpdencmp for signal compression. 
    % find default values (see ddencmp). 
    [thr,sorh,keepapp,crit] = ddencmp('cmp','wp',x)

thr =
    0.5193

sorh =
h

keepapp =
    1

crit =
    threshold

    % Denoise signal using global thresholding with 
    % threshold best basis. 
    [xc,treed,datad,perf0,perfl2] = ... 
    wpdencmp(x,sorh,3,'db2',crit,thr,keepapp);




% Load original image. 
    load sinsin

% Generate noisy image. 
    init = 2055615866; randn('seed',init); 
    x = X/18 + randn(size(X));

% Use wpdencmp for image de-noising. 
    % find default values (see ddencmp). 
    [thr,sorh,keepapp,crit] = ddencmp('den','wp',x)

thr =
    4.9685

sorh =
h

keepapp =
    1

crit =
sure    
% Denoise image using global thresholding with 
% SURE best basis. 
xd = wpdencmp(x,sorh,3,'sym4',crit,thr,keepapp);




% Generate heavy sine and a noisy version of it.
    [xref,x] = wnoise(5,11,7,init);

% Use wpdencmp for signal de-noising. 
    n = length(x); 
    thr = sqrt(2*log(n*log(n)/log(2))); 
    xwpd = wpdencmp(x,'s',4,'sym4','sure',thr,1);

% Compare with wavelet-based de-noising result. 
    xwd = wden(x,'rigrsure','s','one',4,'sym4');