Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

De-noising or compression

`[XC,CXC,LXC,PERF0,PERFL2] = wdencmp('gbl',X,`

* 'wname'*,N,THR,SORH,KEEPAPP)

wdencmp('gbl',C,L,

`'wname'`

[XC,CXC,LXC,PERF0,PERFL2] = wdencmp('lvd',X,

`'wname'`

[XC,CXC,LXC,PERF0,PERFL2] = wdencmp('lvd',C,L,

`'wname'`

[XC,CXC,LXC,PERF0,PERFL2] = wdencmp('lvd',X,

`'wname'`

[XC,CXC,LXC,PERF0,PERFL2] = wdencmp('lvd',C,L,

`'wname'`

`wdencmp`

is a one- or
two-dimensional de-noising and compression-oriented function.

`wdencmp`

performs a de-noising
or compression process of a signal or an image, using wavelets.

`[XC,CXC,LXC,PERF0,PERFL2] = wdencmp('gbl',X,`

returns
a de-noised or compressed version * 'wname'*,N,THR,SORH,KEEPAPP)

`XC`

of input signal `X`

(one-
or two-dimensional) obtained by wavelet coefficients thresholding
using global positive threshold `THR`

.Additional output arguments `[CXC,LXC]`

are
the wavelet decomposition structure of `XC`

(see `wavedec`

or `wavedec2`

for
more information). `PERF0`

and `PERFL2`

are * L^{2}* -norm
recovery and compression score in percentage.

`PERFL2`

= 100 * (vector-norm of `CXC`

/
vector-norm of `C`

)^{2} if `[C,L]`

denotes
the wavelet decomposition structure of `X`

.

If `X`

is a one-dimensional signal and * 'wname'* an
orthogonal wavelet,

`PERFL2`

is reduced to$$\frac{100{\Vert XC\Vert}^{2}}{{\Vert X\Vert}^{2}}$$

Wavelet decomposition is performed at level `N`

and * 'wname'* is
a character vector containing wavelet name (see

`wmaxlev`

and `wfilters`

for more information). `SORH`

(`'s'`

or `'h'`

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

for
more information). If `KEEPAPP`

= 1, approximation
coefficients cannot be thresholded, otherwise it is possible. `wdencmp('gbl',C,L,`

has
the same output arguments, using the same options as above, but obtained
directly from the input wavelet decomposition structure * 'wname'*,N,THR,SORH,KEEPAPP)

`[C,L]`

of
the signal to be de-noised or compressed, at level `N`

and
using `'wname'`

For the one-dimensional case and `'lvd'`

option, ```
[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',X,
```

or * 'wname'*,N,THR,SORH)

```
[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',C,L,
````'wname'`

,N,THR,SORH)

have
the same output arguments, using the same options as above, but allowing
level-dependent thresholds contained in vector `THR`

(`THR`

must
be of length `N`

). In addition, the approximation
is kept. Note that, with respect to `wden`

(automatic
de-noising), `wdencmp`

allows
more flexibility and you can implement your own de-noising strategy.For the two-dimensional case and `'lvd'`

option, ```
[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',X,
```

or * 'wname'*,N,THR,SORH)

```
[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',C,L,
````'wname'`

,N,THR,SORH)

.`THR`

must be a matrix 3 by `N`

containing
the level-dependent thresholds in the three orientations, horizontal,
diagonal, and vertical.

Like denoising, the compression procedure contains three steps:

Decomposition.

Detail coefficient thresholding. For each level from 1 to

`N`

, a threshold is selected and hard thresholding is applied to the detail coefficients.Reconstruction.

The difference with the denoising procedure is found in step 2.

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.

Donoho, D.L.; I.M. Johnstone, "Ideal de-noising in an orthonormal basis chosen from a library of bases," C.R.A.S. Paris, t. 319, Ser. I, pp. 1317–1322.

Donoho, D.L. (1995), "De-noising by soft-thresholding," *IEEE
Trans. on Inf. Theory*, 41, 3, pp. 613–627.

Was this topic helpful?