Multisignal 1-D compression using wavelets
[XC,DECCMP,THRESH] = mswcmp('cmp',DEC,METH)
[XC,DECCMP,THRESH] = mswcmp('cmp',DEC,METH,PARAM)
[XC,THRESH] = mswcmp('cmpsig',...)
[DECCMP,THRESH] = mswcmp('cmpdec',...)
THRESH = mswcmp('thr',...)
[...] = mswcmp(OPTION,DIRDEC,X,WNAME,LEV,METH)
[...] = mswcmp(OPTION,DIRDEC,X,WNAME,LEV,METH,PARAM)
[...] = mswcmp(...,S_OR_H)
[...] = mswcmp(...,S_OR_H,KEEPAPP)
[...] = mswcmp(...,S_OR_H,KEEPAPP,IDXSIG)
mswcmp
computes thresholds
and, depending on the selected option, performs compression of 1-D
signals using wavelets.
[XC,DECCMP,THRESH] = mswcmp('cmp',DEC,METH)
or
[XC,DECCMP,THRESH] = mswcmp('cmp',DEC,METH,PARAM)
returns a compressed (indicated by 'cmp'
input)
version XC
of the original multisignal matrix X
,
whose wavelet decomposition structure is DEC
. The
output XC
is obtained by thresholding the wavelet
coefficients: DECCMP
, which is the wavelet decomposition
associated with XC
(see mdwtdec
),
and THRESH
is the matrix of threshold values. The
input METH
is the name of the compression method
and PARAM
is the associated parameter, if required.
Valid compression methods METH are shown in the following tables.
For methods that use an associated parameter, the range of allowable PARAM
values
is also shown.
'rem_n0' | Remove near 0 |
'bal_sn' | Balance sparsity-norm |
'sqrtbal_sn' | Balance sparsity-norm ( |
'scarce' | Scarce, |
'scarcehi' | Scarce high, |
'scarceme' | Scarce medium, |
'scarcelo' | Scarce low, |
PARAM
is a sparsity parameter, and it should
be such that: 1
≤ PARAM
≤ 10
.
For scarce method no control is done.
'L2_perf' | Energy ratio |
'N0_perf' | Zero coefficients ratio |
PARAM
is a real number which represents the
required performance:
0
≤ PARAM
≤ 100
.
'glb_thr' | Global threshold |
PARAM
is a real positive number.
'man_thr' | Manual method |
PARAM
is an NbSIG
-by-NbLEV
matrix
or NbSIG
-by-(NbLEV+1
) matrix
such that:
- PARAM(i,j)
is the threshold for
the detail coefficients of level j
for the ith
signal (1
≤ j
≤ NbLEV
).
- PARAM(i,NbLEV+1)
is the threshold
for the approximation coefficients for the i
th
signal (if KEEPAPP
is 0
).
Where NbSIG
is the number of signals and NbLEV
the
number of levels of decomposition.
[XC,THRESH] = mswcmp('cmpsig',...)
or
[DECCMP,THRESH] = mswcmp('cmpdec',...)
or
THRESH = mswcmp('thr',...)
Instead
of the 'cmp'
input OPTION
, you
can use 'cmpsig'
, 'cmpdec'
or 'thr'
to select other output arguments. 'thr'
returns
the computed thresholds, but compression is not performed.
[...] = mswcmp(OPTION,DIRDEC,X,WNAME,LEV,METH)
The decomposition structure input argument
[...] = mswcmp(OPTION,DIRDEC,X,WNAME,LEV,METH,PARAM) DEC
can
be replaced by four arguments: DIRDEC
, X
, WNAME
,
and LEV
. Before performing a compression or computing
thresholds, the multisignal matrix X
is decomposed
at level LEV
using the wavelet WNAME
,
in the direction DIRDEC
.
[...] = mswcmp(...,S_OR_H)
Three more optional inputs may be used:
[...] = mswcmp(...,S_OR_H,KEEPAPP)
[...] = mswcmp(...,S_OR_H,KEEPAPP,IDXSIG)
S_OR_H ('s' or 'h')
stands for
soft or hard thresholding (see mswthresh
for
more details). Default is 'h'
.
KEEPAPP (true or false)
indicates
whether to keep approximation coefficients (true
)
or not (false
). Default is false
.
IDXSIG
is a vector which contains
the indices of the initial signals, or the character vector 'all'
.
Default is 'all'
.
% Load original 1D-multisignal. load thinker % Perform a decomposition at level 2 using wavelet db2. dec = mdwtdec('r',X,2,'db2'); % Compress the signals to obtain a percentage of zeros % near 95% for the wavelet coefficients. [XC,decCMP,THRESH] = mswcmp('cmp',dec,'N0_perf',95); [Ecmp,PECcmp,PECFScmp] = wdecenergy(decCMP); % Plot the original signals 1 and 31, and % the corresponding compressed signals. figure; plot(X([1 31],:)','r--','linewidth',2); hold on plot(XC([1 31],:)','b','linewidth',2); grid; set(gca,'Xlim',[1,96]) title('X dashed line and XC solid line')
Birgé L.; P. Massart (1997), “From Model Selection to Adaptive Estimation,” in D. Pollard (ed), Festchrift for L. Le Cam, Springer, pp. 55–88.
DeVore, R.A.; B. Jawerth, B.J. Lucier (1992), “Image Compression Through Wavelet Transform Coding,” IEEE Trans. on Inf. Theory, vol. 38, No 2, pp. 719–746.
Donoho, D.L. (1993), “Progress in Wavelet Analysis and WVD: a Ten Minute Tour,” in Progress in Wavelet Analysis and Applications, Y. Meyer, S. Roques, pp. 109–128. Frontières Ed.
Donoho, D.L.; I.M. Johnstone(1994), “Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika, vol. 81, pp. 425–455.
Donoho, D.L.; I.M. Johnstone, G. Kerkyacharian, D. Picard (1995), “Wavelet Shrinkage: Asymptopia,” Jour. Roy. Stat. Soc., series B, vol. 57 no. 2, pp. 301–369.
Donoho, D.L.; I.M. Johnstone, “Ideal De-noising in an Orthonormal Basis Chosen from a Library of Bases,” C.R.A.S. Paris, t. 319, Ser. I, pp. 1317–1322.
Donoho, D.L. (1995), “De-noising by Soft-thresholding,” IEEE Trans. on Inf. Theory, 41, 3, pp. 613–627.