## Documentation Center |

De-noising or compression using wavelet packets

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

`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 decomposition are the same as those used in the
wavelets framework (see `wden` and `wdencmp` for more information).

`[XD,TREED,PERF0,PERFL2] = wpdencmp(X,SORH,N,'wname',CRIT,PAR,KEEPAPP)` returns
a de-noised or compressed version

The additional output argument `TREED` is the
wavelet packet best tree decomposition (see `besttree` for
more information) of `XD`. `PERFL2` and `PERF0` are *L ^{2}* energy
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,

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

Wavelet packet decomposition is performed at level `N` and * 'wname'* is
a string containing the wavelet name. Best decomposition is performed
using entropy criterion defined by string

`[XD,TREED,PERF0,PERFL2] = wpdencmp(TREE,SORH,CRIT,PAR,KEEPAPP)` has
the same output arguments, using the same options as above, but obtained
directly from the input wavelet packet tree decomposition `TREE` (see `wpdec` for more information) of the signal
to be de-noised or compressed.

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

% The current extension mode is zero-padding (seedwtmode). % Load original signal. load sumlichr; x = sumlichr; % Use wpdencmp for signal compression. % Find default values (seeddencmp). [thr,sorh,keepapp,crit] = ddencmp('cmp','wp',x) thr = 0.5193 sorh = h keepapp = 1 crit = threshold % De-noise signal using global thresholding with % threshold best basis. [xc,wpt,perf0,perfl2] = ... wpdencmp(x,sorh,3,'db2',crit,thr,keepapp); % Using some plotting commands, % the following figure is generated.

% Load original image. load sinsin % Generate noisy image. x = X/18 + randn(size(X)); % Use wpdencmp for image de-noising. % Find default values (seeddencmp). [thr,sorh,keepapp,crit] = ddencmp('den','wp',x) thr = 4.9685 sorh = h keepapp = 1 crit = sure % De-noise image using global thresholding with % SURE best basis. xd = wpdencmp(x,sorh,3,'sym4',crit,thr,keepapp); % Using some plotting commands, % the following figure is generated.

% Generate heavy sine and a noisy version of it. init = 1000; [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');

Antoniadis, A.; G. Oppenheim, Eds. (1995), *Wavelets
and statistics*, Lecture Notes in Statistics, 103, Springer
Verlag.

Coifman, R.R.; M.V. Wickerhauser (1992), "Entropy-based
algorithms for best basis selection," *IEEE Trans.
on Inf. Theory*, vol. 38, 2, pp. 713–718.

DeVore, R.A.; B. Jawerth, B.J. Lucier (1992), "Image
compression through wavelet transform coding," *IEEE
Trans. on Inf. Theory*, vol. 38, No 2, pp. 719–746.

Donoho, D.L. (1993), "Progress in wavelet analysis and WVD: a ten minute tour," in Progress in wavelet analysis and applications, Y. Meyer, S. Roques, pp. 109–128. Frontières Ed.

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, G. Kerkyacharian, D. Picard (1995),
"Wavelet shrinkage: asymptopia," *Jour. Roy.
Stat. Soc.*, series B, vol. 57 no. 2, pp. 301–369.

`besttree` | `ddencmp` | `wdencmp` | `wenergy` | `wpbmpen` | `wpdec` | `wpdec2` | `wthresh `

Was this topic helpful?