ddencmp :: Functions (Wavelet Toolbox™)

ddencmp

Purpose

Default values for de-noising or compression

Syntax

[THR,SORH,KEEPAPP,CRIT] = ddencmp(IN1,IN2,X)
[THR,SORH,KEEPAPP] = ddencmp(IN1,'wv',X)
[THR,SORH,KEEPAPP,CRIT] = ddencmp(IN1,'wp',X)

Description

ddencmp is a de-noising and compression-oriented function.

ddencmp gives default values for all the general procedures related to de-noising and compression of one- or two-dimensional signals, using wavelets or wavelet packets.

[THR,SORH,KEEPAPP,CRIT] = ddencmp(IN1,IN2,X) returns default values for de-noising or compression, using wavelets or wavelet packets, of an input vector or matrix X, which can be a one- or two-dimensional signal. THR is the threshold, SORH is for soft or hard thresholding, KEEPAPP allows you to keep approximation coefficients, and CRIT (used only for wavelet packets) is the entropy name (see wentropy for more information).

IN1 is 'den' for de-noising or 'cmp' for compression.

IN2 is 'wv' for wavelet or 'wp' for wavelet packet.

For wavelets (three output arguments):

[THR,SORH,KEEPAPP] = ddencmp(IN1,'wv',X) returns default values for de-noising (if IN1 = 'den') or compression (if IN1 = 'cmp') of X. These values can be used for wdencmp.

For wavelet packets (four output arguments):

[THR,SORH,KEEPAPP,CRIT] = ddencmp(IN1,'wp',X) returns default values for de-noising (if IN1 = 'den') or compression (if IN1 = 'cmp') of X. These values can be used for wpdencmp.

Examples

% The current extension mode is zero-padding (see dwtmode).

% Generate Gaussian white noise. 
init = 2055415866; randn('seed',init); 
x = randn(1,1000);


% Find default values for wavelets (3 output arguments). 
% These values can be used for wdencmp with option 'gbl'.
    % default for de-noising: 
    % soft thresholding and approximation coefficients kept 
    % thr = sqrt(2*log(n)) * s
    % where s is an estimate of level noise
    % and n is equal to prod(size(x)).
    [thr,sorh,keepapp] = ddencmp('den','wv',x) 

thr =
    3.8593
sorh =
    s
keepapp =
    1

    % default for compression: 
    % hard thresholding and approximation coefficients kept 
    % thr = median(abs(detail at level 1)) if nonzero 
    % else thr = 0.05 * max(abs(detail at level 1)). 
    [thr,sorh,keepapp] = ddencmp('cmp','wv',x)

thr =
    0.7003
sorh =
h
keepapp =
    1

% Find default values for wavelet packets (4 output arguments). 
% These values can be used for wpdencmp.

    % default for de-noising: 
    % soft thresholding and appr. cfs. kept 
    % thr = sqrt(2*log(n*log(n)/log(2)))
    % the noise level is supposed to be equal to 1; 
    % default entropy is 'sure' criterion. 
    [thr,sorh,keepapp,crit] = ddencmp('den','wp',x) 


thr =
    4.2911
sorh =
    h
keepapp =
    1
crit =
    sure

    % default for compression. 
    % hard thresholding and approximation coefficients kept 
    % thr = median(abs(detail at level 1)) 
    % default entropy is 'threshold' criterion. 
    [thr,sorh,keepapp,crit] = ddencmp('cmp','wp',x)

thr =
    0.7003
sorh =
    h
keepapp =
    1
crit =
    threshold

References

Donoho, D.L. (1995), "De-noising by soft-thresholding," IEEE, Trans. on Inf. Theory, 41, 3, pp. 613-627.

Donoho, D.L.; I.M. Johnstone (1994), "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol 81, pp. 425-455.

Donoho, D.L.; I.M. Johnstone (1994), "Ideal de-noising in an orthonormal basis chosen from a library of bases," C.R.A.S. Paris, Ser. I, t. 319, pp. 1317-1322.

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