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ddencmp

Default values for denoising or compression

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

Syntax

``[thr,sorh,keepapp] = ddencmp(in1,in2,x)``
``[___,crit] = ddencmp(in1,'wp',x)``

Description

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.

```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 ```

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.

```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' ```

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.

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

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

 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.

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