# ddencmp

Default values for denoising or compression

## Description

ddencmp returns default values for denoising or compression for the critically sampled discrete wavelet or wavelet packet transform.

example

[thr,sorh,keepapp] = ddencmp(in1,in2,x) returns default values for denoising or compression, using wavelets or wavelet packets, of the input data x. x is a real-valued vector or 2-D matrix. thr is the threshold, and sorh indicates soft or hard thresholding. keepapp can be used as a flag to set whether or not the approximation coefficients are thresholded.

• Set in1 to 'den' for denoising or 'cmp' for compression.

• Set in2 to 'wv' to use wavelets or 'wp' to use wavelet packets.

example

[___,crit] = ddencmp(in1,'wp',x) also returns the entropy type, crit. See wentropy for more information.

## Examples

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Determine the default global denoising threshold for an $N$(0,1) white noise input. Create an $N$(0,1) white noise input. Change the DWT extension mode to periodic. Set the random number generator to the default initial settings for reproducible results.

origmode = dwtmode('status','nodisplay');
dwtmode('per','nodisp')
rng default
x = randn(512,1);

Use ddencmp to obtain the default global threshold for wavelet denoising. Demonstrate that the threshold is equal to the universal threshold of Donoho and Johnstone scaled by a robust estimate of the variance.

[thr,sorh,keepapp] = ddencmp('den','wv',x);
[A,D] = dwt(x,'db1');
noiselev = median(abs(D))/0.6745;
thresh = sqrt(2*log(length(x)))*noiselev;

Compare the value of the variable thr to the value of thresh.

thr
thr = 3.3639
thresh
thresh = 3.3639

Restore the original extension mode.

dwtmode(origmode,'nodisplay')

Determine the default global compression threshold for an $N$(0,1) white noise input.

Create an $N$(0,1) white noise input. Set the DWT extension mode to periodic. Set the random number generator to the default initial settings for reproducible results.

origmode = dwtmode('status','nodisplay');
dwtmode('per','nodisp')
rng default
x = randn(512,1);

Use ddencmp with the 'cmp' and 'wp' input arguments to return the default global compression threshold for a wavelet packet transform.

[thr,sorh,keepapp,crit] = ddencmp('cmp','wp',x)
thr = 0.6424
sorh =
'h'
keepapp = 1
crit =
'threshold'

Compare with the default values returned for denoising.

[thr,sorh,keepapp,crit] = ddencmp('den','wp',x)
thr = 4.1074
sorh =
'h'
keepapp = 1
crit =
'sure'

Restore the original extension mode.

dwtmode(origmode,'nodisplay')

## Input Arguments

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Purpose of ddencmp output, specified as:

• 'den' — Denoising

• 'cmp' — Compression

Transform type to be used for denoising or compression, specified as:

• 'wv' — Critically sampled discrete wavelet transform. This output can be used with wdencmp.

• 'wp' — Critically sampled wavelet packet transform. This output can be used with wpdencmp.

Input data to be denoised or compressed, specified as a real-valued vector or 2-D matrix.

Data Types: double

## Output Arguments

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Threshold for denoising or compression, returned as a real number. Use this output with wdencmp or wpdencmp.

Thresholding type for denoising or compression, returned as a character.

• 's' — Soft thresholding

• 'h' — Hard thresholding

Use this output with wdencmp or wpdencmp.

Threshold approximation setting, returned as 1. Use this output with wdencmp or wpdencmp. If keepapp = 1, the approximation coefficients are not thresholded.

Entropy type when denoising or compressing with wavelet packets, returned as a character vector. Use this output only with wpdencmp. See wentropy for more information.

## References

[1] Donoho, D. L. “De-noising by Soft-Thresholding.” IEEE Transactions on Information Theory, Vol. 42, Number 3, pp. 613–627, 1995.

[2] Donoho, D. L., and Johnstone, I. M. “Ideal Spatial Adaptation by Wavelet Shrinkage.” Biometrika, Vol. 81, pp. 425–455, 1994.

[3] Donoho, D. L., and I. M. Johnstone. "Ideal denoising in an orthonormal basis chosen from a library of bases." Comptes Rendus Acad. Sci. Paris, Ser. I, Vol. 319, pp. 1317–1322, 1994.