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De-noising or compression

`[XC,CXC,LXC,PERF0,PERFL2] = wdencmp('gbl',X,'wname',N,THR,SORH,KEEPAPP)wdencmp('gbl',C,L,'wname',N,THR,SORH,KEEPAPP)[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',X,'wname',N,THR,SORH)[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',C,L,'wname',N,THR,SORH)[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',X,'wname',N,THR,SORH)[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',C,L,'wname',N,THR,SORH)`

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

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,

Wavelet decomposition is performed at level `N` and * 'wname'* is
a string containing wavelet name (see

`wdencmp('gbl',C,L,'wname',N,THR,SORH,KEEPAPP)` has
the same output arguments, using the same options as above, but obtained
directly from the input wavelet decomposition structure

For the one-dimensional case and `'lvd'` option, `[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',X,'wname',N,THR,SORH)` or

For the two-dimensional case and `'lvd'` option, `[XC,CXC,LXC,PERF0,PERFL2]
= wdencmp('lvd',X,'wname',N,THR,SORH)` or

`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:

Detail coefficient thresholding. For each level from 1 to

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

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.

`ddencmp` | `wavedec` | `wavedec2` | `wbmpen` | `wcompress` | `wdcbm2` | `wden` | `wpdencmp` | `wthresh`

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