Inverse 1-D lifting wavelet transform
X = ilwt(AD_In_Place,W)
X = ilwt(CA,CD,W)
X = ilwt(AD_In_Place,W,LEVEL)
X
= ILWT(CA,CD,W,LEVEL)
X = ilwt(AD_In_Place,W,LEVEL,'typeDEC',typeDEC)
X
= ilwt(CA,CD,W,LEVEL,'typeDEC',typeDEC)
ilwt performs a 1-D
lifting wavelet reconstruction with respect to a particular lifted
wavelet that you specify.
X = ilwt(AD_In_Place,W) computes the reconstructed
vector X using the approximation and detail coefficients
vector AD_In_Place obtained by a lifting wavelet
reconstruction. W is a lifted wavelet name (see liftwave).
X = ilwt(CA,CD,W) computes the reconstructed
vector X using the approximation coefficients vector CA and
detail coefficients vector CD obtained by a lifting
wavelet reconstruction.
X = ilwt(AD_In_Place,W,LEVEL) or X
= ILWT(CA,CD,W,LEVEL) computes the lifting wavelet reconstruction,
at level LEVEL.
X = ilwt(AD_In_Place,W,LEVEL,'typeDEC',typeDEC) or X
= ilwt(CA,CD,W,LEVEL,'typeDEC',typeDEC) with typeDEC
= 'w' or 'wp' computes the wavelet or
the wavelet packet decomposition using lifting, at level LEVEL.
Instead of a lifted wavelet name, you may use the associated
lifting scheme LS: X = ilwt(...,LS,...) instead
of X = ILWT(...,W,...).
For more information about lifting schemes, see lsinfo.
% Start from the Haar wavelet and get the
% corresponding lifting scheme.
lshaar = liftwave('haar');
% Add a primal ELS to the lifting scheme.
els = {'p',[-0.125 0.125],0};
lsnew = addlift(lshaar,els);
% Perform LWT at level 1 of a simple signal.
x = 1:8;
[cA,cD] = lwt(x,lsnew);
% Perform integer LWT of the same signal.
lshaarInt = liftwave('haar','int2int');
lsnewInt = addlift(lshaarInt,els);
[cAint,cDint] = lwt(x,lsnewInt);
% Invert the two transforms.
xRec = ilwt(cA,cD,lsnew);
err = max(max(abs(x-xRec)))
err =
4.4409e-016
xRecInt = ilwt(cAint,cDint,lsnewInt);
errInt = max(max(abs(x-xRecInt)))
errInt =
0