# Documentation

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# lwtcoef2

Extract or reconstruct 2-D LWT wavelet coefficients

## Syntax

```Y = lwtcoef2(TYPE,XDEC,LS,LEVEL,LEVEXT) Y = lwtcoef2(TYPE,XDEC,W,LEVEL,LEVEXT) ```

## Description

`Y = lwtcoef2(TYPE,XDEC,LS,LEVEL,LEVEXT)` returns the coefficients or the reconstructed coefficients of level `LEVEXT`, extracted from `XDEC`, the LWT decomposition at level `LEVEL` obtained with the lifting scheme `LS`.

The valid values for `TYPE` are listed in this table.

TYPE Values

Description

`'a'`

Approximations

`'h'`

Horizontal details

`'v'`

Vertical details

`'d'`

Diagonal details

`'ca' `

Coefficients of approximations

`'ch'`

Coefficients of horizontal details

`'cv'`

Coefficients of vertical details

`'cd'`

Coefficients of diagonal details

`Y = lwtcoef2(TYPE,XDEC,W,LEVEL,LEVEXT)` returns the same output using `W`, which is the name of a lifted wavelet.

## 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 2 of a simple image. x = reshape(1:16,4,4); xDec = lwt2(x,lsnew,2) xDec = 27.4375 4.0000 17.0000 4.0000 1.0000 0 1.0000 0 4.2500 4.0000 0.0000 4.0000 1.0000 0 1.0000 0 % Extract approximation coefficients of level 1. ca1 = lwtcoef2('ca',xDec,lsnew,2,1) ca1 = 5.7500 22.7500 10.0000 27.0000 % Reconstruct approximations and details. a1 = lwtcoef2('a',xDec,lsnew,2,1) a1 = 2.8750 2.8750 11.3750 11.3750 2.8750 2.8750 11.3750 11.3750 5.0000 5.0000 13.5000 13.5000 5.0000 5.0000 13.5000 13.5000 a2 = lwtcoef2('a',xDec,lsnew,2,2) a2 = 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 6.8594 h1 = lwtcoef2('h',xDec,lsnew,2,1) h1 = -0.3750 -0.3750 -0.3750 -0.3750 0.6250 0.6250 0.6250 0.6250 -0.5000 -0.5000 -0.5000 -0.5000 0.5000 0.5000 0.5000 0.5000 v1 = lwtcoef2('v',xDec,lsnew,2,1) v1 = -1.5000 2.5000 -2.0000 2.0000 -1.5000 2.5000 -2.0000 2.0000 -1.5000 2.5000 -2.0000 2.0000 -1.5000 2.5000 -2.0000 2.0000 d1 = lwtcoef2('d',xDec,lsnew,2,1) d1 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 h2 = lwtcoef2('h',xDec,lsnew,2,2) h2 = -0.7969 -0.7969 -0.7969 -0.7969 -0.7969 -0.7969 -0.7969 -0.7969 1.3281 1.3281 1.3281 1.3281 1.3281 1.3281 1.3281 1.3281 v2 = lwtcoef2('v',xDec,lsnew,2,2) v2 = -3.1875 -3.1875 5.3125 5.3125 -3.1875 -3.1875 5.3125 5.3125 -3.1875 -3.1875 5.3125 5.3125 -3.1875 -3.1875 5.3125 5.3125 d2 = lwtcoef2('d',xDec,lsnew,2,2) d2 = 1.0e-015 * 0.2498 0.2498 -0.4163 -0.4163 0.2498 0.2498 -0.4163 -0.4163 -0.4163 -0.4163 0.6939 0.6939 -0.4163 -0.4163 0.6939 0.6939 % Check perfect reconstruction. err = max(max(abs(x-a2-h2-v2-d2-h1-v1-d1))) err = 3.5527e-015 ```

## Tips

If XDEC is obtained from an indexed image analysis or a truecolor image analysis, it is an `m`-by-`n` matrix or an `m`-by-`n`-by-3 array, respectively.

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