Multisignal 1-D wavelet compression scores

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

`[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 string`'all'`

.

The defaults are, respectively, `'h'`

, false
and `'all'`

.

% 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');

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.)

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