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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

`SWC = swt2(X,N,'wname')` or

`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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