Wavelet Toolbox |

De-noising or compression using wavelet packets

**Syntax**

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

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

**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 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 `XD`

of input signal `X`

(one- or two-dimensional) obtained by wavelet packets coefficients thresholding.

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 '

' an orthogonal wavelet, *wname*`PERFL2`

is reduced to

`SORH`

(`'s'`

or `'h'`

) is for soft or hard thresholding (see `wthresh`

for more information).

Wavelet packet decomposition is performed at level `N`

and '

' is a string containing the wavelet name. Best decomposition is performed using entropy criterion defined by string *wname*`CRIT`

and parameter `PAR`

(see `wentropy`

for more information). Threshold parameter is also `PAR`

. If `KEEPAPP`

= 1, approximation coefficients cannot be thresholded; otherwise, they can be.

`[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.

**Examples**

% The current extension mode is zero-padding (see

`dwtmode`

). % 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 % De-noise signal using global thresholding with % threshold best basis. [xc,treed,datad,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. 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 % 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. [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'); % Using some plotting commands, % the following figure is generated.

**See Also**

`besttree, ddencmp, wdencmp, wenergy, wpbmpen, wpdec, wpdec2,`

`wthresh`

**References **

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.

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