Wavelet Toolbox |

Single-level discrete 2-D wavelet transform

**Syntax **

**Description **

The `dwt2`

command performs a single-level two-dimensional wavelet decomposition with respect to either a particular wavelet ('

', see *wname*`wfilters`

` `

for more information) or particular wavelet decomposition filters (`Lo_D`

and `Hi_D`

) you specify.

`[cA,cH,cV,cD] = dwt2(X,`

'

'*wname*`)`

computes the approximation coefficients matrix `cA`

and details coefficients matrices `cH`

, `cV`

, and `cD`

(horizontal, vertical, and diagonal, respectively), obtained by wavelet decomposition of the input matrix `X`

. The '

' string contains the wavelet name.*wname*

`[cA,cH,cV,cD] = dwt2(X,Lo_D,Hi_D)`

computes the two-dimensional wavelet decomposition as above, based on wavelet decomposition filters that you specify.

`Lo_D`

and `Hi_D`

must be the same length.

Let `sx = size(X)`

and `lf = `

the length of filters; then `size(cA) = size(cH) = size(cV) = size(cD) = sa`

where `sa = ceil(sx/2)`

,` `

if the DWT extension mode is set to periodization.` `

For the other extension modes, `sa = floor((sx+lf-1)/2).`

For information about the different Discrete Wavelet Transform extension modes, see `dwtmode`

.

`[cA,cH,cV,cD] = dwt2(...,`

'`mode`

'`,MODE)`

computes the wavelet decomposition with the extension mode `MODE`

that you specify.

`MODE`

is a string containing the desired extension mode.

**Examples**

% The current extension mode is zero-padding (see

`dwtmode`

). % Load original image. load woman; % X contains the loaded image. % map contains the loaded colormap. nbcol = size(map,1); % Perform single-level decomposition % of X using db1. [cA1,cH1,cV1,cD1] = dwt2(X,'db1'); % Images coding. cod_X = wcodemat(X,nbcol); cod_cA1 = wcodemat(cA1,nbcol); cod_cH1 = wcodemat(cH1,nbcol); cod_cV1 = wcodemat(cV1,nbcol); cod_cD1 = wcodemat(cD1,nbcol); dec2d = [... cod_cA1, cod_cH1; ... cod_cV1, cod_cD1 ... ]; % Using some plotting commands, % the following figure is generated.

**Algorithm **

For images, there exist an algorithm similar to the one-dimensional case for two-dimensional wavelets and scaling functions obtained from one- dimensional ones by tensorial product.

This kind of two-dimensional DWT leads to a decomposition of approximation coefficients at level *j* in four components: the approximation at level *j* + 1, and the details in three orientations (horizontal, vertical, and diagonal).

The following chart describes the basic decomposition steps for images:

**See Also**

```
dwtmode, idwt2, wavedec2, waveinfo
```

**References**

Daubechies, I. (1992), *Ten lectures on wavelets*, CBMS-NSF conference series in applied mathematics. SIAM Ed.

Mallat, S. (1989),"A theory for multiresolution signal decomposition: the wavelet representation," *IEEE Pattern Anal. and Machine Intell.*, vol. 11, no. 7, pp. 674-693.

Meyer, Y. (1990), *Ondelettes et opérateurs*, Tome 1, Hermann Ed. (English translation: *Wavelets and operators*, Cambridge Univ. Press. 1993.)

dwt | dwtmode |