ddencmp

Default values for denoising or compression

Syntax

[thr,sorh,keepapp] = ddencmp(in1,in2,x)

[___,crit] = ddencmp(in1,'wp',x)

Description

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

[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.

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

Examples

Default Global Threshold for Wavelet Denoising

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')

Default Global Threshold for Wavelet Packet Compression

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

in1 — Purpose

'den' | 'cmp'

Purpose of ddencmp output, specified as:

• 'den' — Denoising

• 'cmp' — Compression

in2 — Transform type

'wv' | 'wp'

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.

x — Input data

real-valued vector or matrix

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

Data Types: double

Output Arguments

thr — Threshold

real number

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

sorh — Thresholding type

character

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

• 's' — Soft thresholding

• 'h' — Hard thresholding

Use this output with wdencmp or wpdencmp.

keepapp — Threshold approximation setting

1 (default)

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

crit — Entropy type

character vector

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Variable-size data support must be enabled.

Version History

Introduced before R2006a