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swt2

Discrete stationary wavelet transform 2-D

Syntax

Description

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,'wname') or [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 2N 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 above, given these filters as input:

Lo_D and Hi_D must be the same length.

Examples

Algorithm

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

This kind of two-dimensional SWT 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 step for images:

See Also
dwt2, wavedec2

References

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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