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Denoising or compression

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

`[___] = wdencmp('gbl',C,L,wname,N,THR,SORH,KEEPAPP)`

`[___] = wdencmp('lvl',X,wname,N,THR,SORH)`

`[___] = wdencmp('lvl',C,L,wname,N,THR,SORH)`

`[`

returns a denoised or compressed version `XC`

,`CXC`

,`LXC`

,`PERF0`

,`PERFL2`

] = wdencmp('gbl',`X`

,`wname`

,`N`

,`THR`

,`SORH`

,`KEEPAPP`

)`XC`

of the input data
`X`

obtained by wavelet coefficients thresholding using the
global positive threshold `THR`

. `X`

is a
real-valued vector or matrix. [`CXC`

,`LXC`

] is
the `N`

-level wavelet decomposition structure of
`XC`

(see `wavedec`

or `wavedec2`

for more information).
`PERFL2`

and `PERF0`

are the
*L*^{2}-norm recovery and compression
scores in percentages, respectively. If `KEEPAPP`

= 1, the
approximation coefficients are kept. If `KEEPAPP`

= 0, the
approximation coefficients can be thresholded.

The denoising and compression procedures contain three steps:

Decomposition.

Thresholding.

Reconstruction.

The two procedures differ in Step 2. In compression, for each level in the wavelet decomposition, a threshold is selected and hard thresholding is applied to the detail coefficients.

[1] DeVore, R. A., B. Jawerth, and
B. J. Lucier. “Image Compression Through Wavelet Transform Coding.”
*IEEE Transactions on Information Theory*. Vol. 38, Number 2,
1992, pp. 719–746.

[2] Donoho, D. L. “Progress
in Wavelet Analysis and WVD: A Ten Minute Tour.” *Progress in Wavelet
Analysis and Applications* (Y. Meyer, and S. Roques, eds.).
Gif-sur-Yvette: Editions Frontières, 1993.

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

[4] Donoho, D. L., I. M.
Johnstone, G. Kerkyacharian, and D. Picard. “Wavelet Shrinkage:
Asymptopia?” *Journal of the Royal Statistical Society*,
*series B*, Vol. 57, No. 2, pp. 301–369, 1995.

[5] Donoho, D. L., and I. M.
Johnstone. “Ideal denoising in an orthonormal basis chosen from a library of
bases.” *C. R. Acad. Sci. Paris*, *Ser. I*,
Vol. 319, pp. 1317–1322, 1994.

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