Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

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 real-valued 2-D or 3-D matrix `X`

at
level `N`

, using `'wname'`

If `X`

is a 3-D matrix, the third dimension of `X`

must
equal 3.

`N`

must be a strictly positive integer (see `wmaxlev`

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

and `size(X,2)`

.

The dimension of `X`

and level `N`

determine the
dimensions of the outputs.

If

`X`

is a 2-D matrix and`N`

is greater than 1, the 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)]

If

`X`

is a 2-D matrix and`N`

is equal to 1, the outputs`[A,H,V,D]`

are 2-D arrays where`A`

contains the approximation coefficients, and`H`

,`V`

, and`D`

contain the horizontal, vertical, and diagonal detail coefficients, respectively.If

`X`

is a 3-D matrix of dimension`m`

-by-`n`

-by-3, and`N`

is greater than 1, the outputs`[A,H,V,D]`

are 4-D arrays of dimension`m`

-by-`n`

-by-3-by-`N`

, which contain the coefficients:For

`1`

≤`i`

≤`N`

and`j = 1, 2, 3`

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

contains the coefficients of approximation of level`i`

.The output matrices

`H(:,:,j,i)`

,`V(:,:,j,i)`

and`D(:,:,j,i)`

contain the coefficients of details of level`i`

(horizontal, vertical, and diagonal):SWC = [H(:,:,1:3,1:N) ; V(:,:,1:3,1:N) ; D(:,:,1:3,1:N) ; A(:,:,1:3,N)]

If

`X`

is a 3-D matrix of dimension`m`

-by-`n`

-by-3, and`N`

is equal to 1, the outputs`[A,H,V,D]`

are 4-D arrays of dimension`m`

-by-`n`

-by-1-by-3, which contain the coefficients:For

`j = 1, 2, 3`

, the output matrix`A(:,:,1,j)`

contains the approximation coefficients.The output matrices

`H(:,:,1,j)`

,`V(:,:,1,j)`

and`D(:,:,1,j)`

contain the horizontal, vertical, and diagonal detail coefficients, respectively.SWC = [H(:,:,1,1:3) ; V(:,:,1,1:3) ; D(:,:,1,1:3) ; A(:,:,1,1:3)]

`swt2`

uses double-precision arithmetic internally and returns double-precision coefficient matrices.`swt2`

warns if there is a loss of precision when converting to double.To distinguish a single-level decomposition of a truecolor image from a multilevel decomposition of an indexed image, the approximation and detail coefficient arrays of truecolor images are 4-D arrays. See the Release Notes for details. Also see examples Stationary Wavelet Transform of an Image and Inverse Stationary Wavelet Transform of an Image.

If an

`K`

-level decomposition is performed, the dimensions of the`A`

,`H`

,`V`

, and`D`

coefficient arrays are`m`

-by-`n`

-by-3-by-`K`

.If a single-level decomposition is performed, the dimensions of the

`A`

,`H`

,`V`

, and`D`

coefficient arrays are`m`

-by-`n`

-by-1-by-3. Since MATLAB^{®}removes singleton last dimensions by default, the third dimension of the coefficient arrays is singleton.

`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.

`swt2`

is defined using periodic extension.
The size of the approximation and details coefficients computed at each level equals the
size of the input data.

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

-by-`n`

matrix. If the level of decomposition `N`

is greater than 1, the output
arrays SWC or cA, cH, cV, and cD are
`m`

-by-`n`

-by-`N`

arrays. If the level of
decomposition `N`

is equal to 1, the output arrays SWC or cA, cH, cV, and cD
are `m`

-by-`n`

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. If the level of decomposition
`N`

is greater than 1, the output arrays SWC or cA, cH, cV, and cD are
`m`

-by-`n`

-by-3-by-`N`

. If the level of
decomposition `N`

is equal to 1, the output arrays SWC or cA, cH, cV, and cD
are `m`

-by-`n`

-by-1-by-3.

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
*j*+1, and the details in three orientations (horizontal, vertical, and
diagonal).

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.

Was this topic helpful?