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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 row-wise if DEC.dirDec is equal to 'r' or column-wise 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) (2jNbCFS), and L2SCR(:,1)=100.

  • N0SCR(i,j) is the percentage of zeros corresponding to a threshold equal to CFS(i,j-1) (2jNbCFS), 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 'all'.

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

Examples

collapse all

Load the 23 channel EEG data Espiga3 [4]. The channels are arranged column-wise. The data is sampled at 200 Hz.

load Espiga3

Perform a decomposition at level 2 using the db2 wavelet.

dec = mdwtdec('c',Espiga3,2,'db2')
dec = struct with fields:
        dirDec: 'c'
         level: 2
         wname: 'db2'
    dwtFilters: [1x1 struct]
       dwtEXTM: 'sym'
      dwtShift: 0
      dataSize: [995 23]
            ca: [251x23 double]
            cd: {[499x23 double]  [251x23 double]}

Compute the compression performances for soft and hard thresholding.

[THR_S,L2SCR_S,N0SCR_S] = mswcmpscr(dec,'s');
[THR_H,L2SCR_H,N0SCR_H] = mswcmpscr(dec,'h');

References

[1] Daubechies, I. Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia, PA: SIAM Ed, 1992.

[2] Mallat, S. G. “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 11, Issue 7, July 1989, pp. 674–693.

[3] Meyer, Y. Wavelets and Operators. Translated by D. H. Salinger. Cambridge, UK: Cambridge University Press, 1995.

[4] Mesa, Hector. “Adapted Wavelets for Pattern Detection.” In Progress in Pattern Recognition, Image Analysis and Applications, edited by Alberto Sanfeliu and Manuel Lazo Cortés, 3773:933–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. https://doi.org/10.1007/11578079_96.

Introduced in R2007a