mswcmptp

Multisignal 1-D compression thresholds and performances

Syntax

[THR_VAL,L2_Perf,N0_Perf] = mswcmptp(DEC,METH)
[THR_VAL,L2_Perf,N0_Perf] = mswcmptp(DEC,METH,PARAM)

Description

[THR_VAL,L2_Perf,N0_Perf] = mswcmptp(DEC,METH) or [THR_VAL,L2_Perf,N0_Perf] = mswcmptp(DEC,METH,PARAM) computes the vectors THR_VAL, L2_Perf and N0_Perf obtained after a compression using the METH method and, if required, the PARAM parameter (see mswcmp for more information on METH and PARAM).

For the ith signal:

  • THR_VAL(i) is the threshold applied to the wavelet coefficients. For a level dependent method, THR_VAL(i,j) is the threshold applied to the detail coefficients at level j

  • L2_Perf(i) is the percentage of energy (L2_norm) preserved after compression.

  • N0_Perf(i) is the percentage of zeros obtained after compression.

You can use three more optional inputs:

[...] = mswcmptp(...,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 which contains the indices of the initial signals, or the string '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 thresholds and exact performances 
% obtained after a compression using the method 'N0_perf' and
% requiring a percentage of zeros near 95% for the wavelet
% coefficients.
[THR_VAL,L2_Perf,N0_Perf] = mswcmptp(dec,'N0_perf',95);

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.)

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