# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

# mswcmpscr

Multisignal 1-D wavelet compression scores

## Syntax

```[THR,L2SCR,NOSCR,IDXSORT] = mswcmpscr(DEC) ```

## Description

`[THR,L2SCR,NOSCR,IDXSORT] = mswcmpscr(DEC)` computes four matrices: thresholds `THR`, compression scores `L2SCR` and `NOSCR`, and indices `IDXSORT`. The decomposition `DEC` corresponds to a matrix of wavelet coefficients `CFS` obtained by concatenation of detail and (optionally) approximation coefficients, where

`CFS = [cd{DEC.level}, ... , cd{1}]` or ```CFS = [ca, cd{DEC.level}, ... , cd{1}]```

The concatenation is made rowwise if `DEC.dirDec` is equal to `'r'` or columnwise if `DEC.dirDec` is equal to `'c'` .

If `NbSIG` is the number of original signals and `NbCFS` the number of coefficients for each signal (all or only the detail coefficients), then `CFS` is an `NbSIG`-by-`NbCFS` matrix. Therefore,

• `THR`, `L2SCR`, `NOSCR` are `NbSIG`-by-(`NbCFS+1`) matrices

• `IDXSORT` is an `NbSIG`-by-`NbCFS` matrix

• `THR(:,2:end)` is equal to `CFS` sorted by row in ascending order with respect to the absolute value.

• For each row, `IDXSORT` contains the order of coefficients and `THR(:,1)=0`.

For the ith signal:

• `L2SCR(i,j)` is the percentage of preserved energy (L2-norm), corresponding to a threshold equal to `CFS(i,j-1)` (`2``j``NbCFS`), and `L2SCR(:,1)=100`.

• `N0SCR(i,j)` is the percentage of zeros corresponding to a threshold equal to `CFS(i,j-1)` (`2``j``NbCFS`), and `N0SCR(:,1)=0`.

Three more optional inputs may be used:

`[...] = mswcmpscr(...,S_OR_H,KEEPAPP,IDXSIG)`

• `S_OR_H ('s' or 'h')` stands for soft or hard thresholding (see `mswthresh` for more details).

• `KEEPAPP (true or false)` indicates whether to keep approximation coefficients (`true`) or not (`false`).

• `IDXSIG` is a vector that contains the indices of the initial signals, or the character vector `'all'`.

The defaults are, respectively, `'h'`, false and `'all'`.

## Examples

```% Load original 1D-multisignal. load thinker % Perform a decomposition at level 2 using wavelet db2. dec = mdwtdec('r',X,2,'db2'); % Compute compression performances for soft an hard thresholding. [THR_S,L2SCR_S,N0SCR_S] = mswcmpscr(dec,'s'); [THR_H,L2SCR_H,N0SCR_H] = mswcmpscr(dec,'h'); ```

## References

Daubechies, I. (1992), Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics. SIAM Ed.

Mallat, S. (1989), “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Pattern Anal. and Machine Intell., vol. 11, no. 7, pp. 674–693.

Meyer, Y. (1990), Ondelettes et opérateurs, Tome 1, Hermann Ed. (English translation: Wavelets and operators, Cambridge Univ. Press. 1993.)