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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 an orthogonal or
a biorthogonal wavelet. Specify the wavelet using its name(* 'wname'*,
see

`wfilters`

for more information)
or its 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.

When X represents an indexed image, X is an `m`

-by-`n`

matrix
and the output arrays SWC or cA,cH,cV, and cD are `m`

-by-`n`

-by-`p`

arrays.

When X represents a truecolor image, it becomes an `m`

-by-`n`

-by-3
array. This array is an `m`

-by-`n`

-by-3
array, where each `m`

-by-`n`

matrix
represents a red, green, or blue color plane concatenated along the
third dimension. The output arrays SWC or cA,cH,cV, and cD are `m`

-by-`n`

-by-`p`

-by-3
arrays.

For more information on image formats, see the `image`

and `imfinfo`

reference
pages.

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

The following chart describes the basic decomposition step for images:

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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