# Documentation

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# ilwt2

Inverse 2-D lifting wavelet transform

## Syntax

```X = ilwt2(AD_In_Place,W) X = ilwt2(CA,CH,CV,CD,W) X = ilwt2(AD_In_Place,W,LEVEL) X = ILWT2(CA,CH,CV,CD,W,LEVEL) X = ilwt2(AD_In_Place,W,LEVEL,'typeDEC',typeDEC) X = ilwt2(CA,CH,CV,CD,W,LEVEL,'typeDEC',typeDEC) ```

## Description

`ilwt2` performs a 2-D lifting wavelet reconstruction with respect to a particular lifted wavelet that you specify.

`X = ilwt2(AD_In_Place,W)` computes the reconstructed matrix `X` using the approximation and detail coefficients matrix `AD_In_Place`, obtained by a lifting wavelet decomposition. `W` is a lifted wavelet name (see `liftwave`).

`X = ilwt2(CA,CH,CV,CD,W)` computes the reconstructed matrix `X` using the approximation coefficients vector `CA` and detail coefficients vectors `CH`, `CV`, and `CD` obtained by a lifting wavelet decomposition.

`X = ilwt2(AD_In_Place,W,LEVEL)` or ```X = ILWT2(CA,CH,CV,CD,W,LEVEL)``` computes the lifting wavelet reconstruction, at level `LEVEL`.

`X = ilwt2(AD_In_Place,W,LEVEL,'typeDEC',typeDEC)` or ```X = ilwt2(CA,CH,CV,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 = ilwt2(...,LS,...)` instead of `X = ilwt2(...,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); % Perform integer LWT of the same image. lshaarInt = liftwave('haar','int2int'); lsnewInt = addlift(lshaarInt,els); [cAint,cHint,cVint,cDint] = lwt2(x,lsnewInt); % Invert the two transforms. xRec = ilwt2(cA,cH,cV,cD,lsnew); err = max(max(abs(x-xRec))) err = 0 xRecInt = ilwt2(cAint,cHint,cVint,cDint,lsnewInt); errInt = max(max(abs(x-xRecInt))) errInt = 0 ```

## Tips

If `AD_In_Place` or cA,cH,cV,cD are obtained from an indexed image analysis or a truecolor image analysis, they are `m`-by-`n` matrices or `m`-by-`n`-by-3 arrays, respectively.

For more information on image formats, see the `image` and `imfinfo` reference pages.