lwt2 (Wavelet Toolbox)

2-D lifting wavelet transform

Syntax

[CA,CH,CV,CD] = lwt2(X,W)
X_InPlace = lwt2(X,LS)
lwt2(X,W,LEVEL)
X_InPlace = lwt2(X,W,LEVEL,'typeDEC',typeDEC)
[CA,CD] = lwt2(X,W,LEVEL,'typeDEC',typeDEC)

Description

lwt2 performs a 2-D lifting wavelet decomposition with respect to a particular lifted wavelet that you specify.

[CA,CH,CV,CD] = lwt2(X,W) computes the approximation coefficients matrix CA and detail coefficients matrices CH, CV, and CD, obtained by a lifting wavelet decomposition, of the matrix X. W is a lifted wavelet name (see liftwave).

X_InPlace = lwt2(X,LS) computes the approximation and detail coefficients. These coefficients are stored in place:

CA = X_InPlace(1:2:end,1:2:end)

CH = X_InPlace(2:2:end,1:2:end)

CV = X_InPlace(1:2:end,2:2:end)

CD = X_InPlace(2:2:end,2:2:end)

lwt2(X,W,LEVEL) computes the lifting wavelet decomposition at level LEVEL.

X_InPlace = lwt2(X,W,LEVEL,'typeDEC',typeDEC) or [CA,CH,CV,CD] = LWT2(X,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: lwt2(X,LS,...) instead of LWT2(X,W,...).

For more information about lifting schemes, see lsinfo.

Examples

% 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 image.
x = reshape(1:16,4,4);
[cA,cH,cV,cD] = lwt2(x,lsnew)

cA =

    5.7500   22.7500
   10.0000   27.0000


cH =

    1.0000    1.0000
    1.0000    1.0000


cV =

    4.0000    4.0000
    4.0000    4.0000


cD =

     0     0
     0     0

% Perform integer LWT of the same image.
lshaarInt = liftwave('haar','int2int');
lsnewInt = addlift(lshaarInt,els);
[cAint,cHint,cVint,cDint] = lwt2(x,lsnewInt)

cAint =

     3    11
     5    13


cHint =

     1     1
     1     1


cVint =

     4     4
     4     4


cDint =

     0     0
     0     0

Algorithm

This function implements the polyphase algorithm.

lwt reduces to dwt with zero-padding extension mode and without extra-coefficients.

See Also

ilwt2

References

Strang, G.; T. Nguyen (1996), Wavelets and filter banks, Wellesley-Cambridge Press.

Sweldens, W. (1998), "The Lifting Scheme: a Construction of Second Generation of Wavelets," SIAM J. Math. Anal., 29 (2), pp. 511-546.

lwt lwtcoef