Wavelet Toolbox™

Inverse discrete stationary wavelet transform 2-D

Syntax

• X = iswt2(SWC,'wname')
  X = iswt2(A,H,V,D,'wname')
  X = iswt2(SWC,Lo_R,Hi_R)
  X = iswt2(A,H,V,D,Lo_R,Hi_R)
  

Description

iswt2 performs a multilevel 2-D stationary wavelet reconstruction using either a specific orthogonal wavelet ('wname'--see wfilters for more information) or specific reconstruction filters (Lo_R and Hi_R).

X = iswt2(SWC,'wname') or X = iswt2(A,H,V,D,'wname') or X = iswt2(A(:,:,end),H,V,D,'wname') reconstructs the signal X, based on the multilevel stationary wavelet decomposition structure SWC or [A,H,V,D] (see swt2).

X = iswt2(SWC,Lo_R,Hi_R) or X = iswt2(A,H,V,D,Lo_R,Hi_R) or X = iswt2(A(:,:,end),H,V,D,Lo_R,Hi_R) reconstructs as in the previous syntax, using filters that you specify:

• Lo_R is the reconstruction low-pass filter.
• Hi_R is the reconstruction high-pass filter.

Lo_R and Hi_R must be the same length.

Remarks

If SWC or (cA,cH,cV,cD) are obtained from an indexed image analysis or a truecolor image analysis, then X is an m-by-n matrix or an m-by-n-by-3 array, respectively.

For more information on image formats, see the image and imfinfo reference pages.

Examples

• % Load original image.
  load nbarb1;
                  
  % Perform SWT decomposition
  % of X at level 3 using sym4.
  swc = swt2(X,3,'sym4');
  % Second usage.
  [ca,chd,cvd,cdd] = swt2(X,3,'sym4');
  
  % Reconstruct s from the stationary wavelet
  % decomposition structure swc.
  a0 = iswt2(swc,'sym4');
  % Second usage.
  a0 = iswt2(ca,chd,cvd,cdd,'sym4');
  % Check for perfect reconstruction.
  err = max(max(abs(X-a0)))
  ans =
    2.3482e-010
  
  errbis = max(max(abs(X-a0bis)))
  ans =
    2.3482e-010
  

Algorithm

See the section "Stationary Wavelet Transform" in Chapter 6, "Advanced Concepts", of the User's Guide.

See Also
idwt2, swt2, waverec2

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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