Discrete stationary wavelet transform 2-D

`SWC = swt2(X,N,'`

* wname*')

[A,H,V,D] = swt2(X,N,'

`wname`

SWC = swt2(X,N,Lo_D,Hi_D)

[A,H,V,D] = swt2(X,N,Lo_D,Hi_D)

`swt2`

performs a multilevel
2-D stationary wavelet decomposition using either a specific orthogonal
wavelet (* 'wname'*— see

`wfilters`

for more information) or specific
orthogonal wavelet decomposition filters.`SWC = swt2(X,N,'`

or * wname*')

```
[A,H,V,D]
= swt2(X,N,'
````wname`

')

compute
the stationary wavelet decomposition of the matrix `X`

at
level `N`

, using `'wname'`

`N`

must be a strictly positive integer (see `wmaxlev`

for more information), and 2^{N }must
divide `size(X,1)`

and `size(X,2)`

.

Outputs `[A,H,V,D]`

are 3-D arrays, which contain
the coefficients:

For

`1`

≤`i`

≤`N`

, the output matrix`A(:,:,i)`

contains the coefficients of approximation of level`i`

.The output matrices

`H(:,:,i)`

,`V(:,:,i)`

and`D(:,:,i)`

contain the coefficients of details of level`i`

(horizontal, vertical, and diagonal):SWC = [H(:,:,1:N) ; V(:,:,1:N) ; D(:,:,1:N) ; A(:,:,N)]

`SWC = swt2(X,N,Lo_D,Hi_D)`

or ```
[A,H,V,D]
= swt2(X,N,Lo_D,Hi_D)
```

, computes the stationary wavelet
decomposition as in the previous syntax, given these filters as input:

`Lo_D`

is the decomposition low-pass filter.`Hi_D`

is the decomposition high-pass filter.

`Lo_D`

and `Hi_D`

must be
the same length.

% Load original image. load nbarb1; % Image coding. nbcol = size(map,1); cod_X = wcodemat(X,nbcol); % Visualize the original image. subplot(221) image(cod_X) title('Original image'); colormap(map) % Perform SWT decomposition % of X at level 3 using sym4. [ca,chd,cvd,cdd] = swt2(X,3,'sym4'); % Visualize the decomposition. for k = 1:3 % Images coding for level k. cod_ca = wcodemat(ca(:,:,k),nbcol); cod_chd = wcodemat(chd(:,:,k),nbcol); cod_cvd = wcodemat(cvd(:,:,k),nbcol); cod_cdd = wcodemat(cdd(:,:,k),nbcol); decl = [cod_ca,cod_chd;cod_cvd,cod_cdd]; % Visualize the coefficients of the decomposition % at level k. subplot(2,2,k+1) image(decl) title(['SWT dec.: approx. ', ... 'and det. coefs (lev. ',num2str(k),')']); colormap(map) end % Editing some graphical properties, % the following figure is generated.

Nason, G.P.; B.W. Silverman (1995), "The stationary wavelet
transform and some statistical applications," *Lecture
Notes in Statistics*, 103, pp. 281–299.

Coifman, R.R.; Donoho, D.L. (1995), "Translation invariant
de-noising," *Lecture Notes in Statistics*,
103, pp. 125–150.

Pesquet, J.C.; H. Krim, H. Carfatan (1996), "Time-invariant
orthonormal wavelet representations," *IEEE Trans.
Sign. Proc.*, vol. 44, 8, pp. 1964–1970.

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