Wavelet Toolbox™

Single-level inverse discrete 2-D wavelet transform

Syntax

• X = idwt2(cA,cH,cV,cD,'wname')
  X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R)
  X = idwt2(cA,cH,cV,cD,'wname',S)
  X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R,S)
  X = idwt2(...,'mode',MODE)
  

Description

The idwt2 command performs a single-level two-dimensional wavelet reconstruction with respect to either a particular wavelet ('wname', see wfilters for more information) or particular wavelet reconstruction filters (Lo_R and Hi_R) that you specify.

X = idwt2(cA,cH,cV,cD,'wname') uses the wavelet 'wname' to compute the single-level reconstructed approximation coefficients matrix X, based on approximation matrix cA and details matrices cH,cV, and cD (horizontal, vertical, and diagonal, respectively).

X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R) reconstructs as above, 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.

Let sa = size(cA) = size(cH) = size(cV) = size(cD) and lf the length of the filters; then size(X) = SX, where SX = 2* SA, if the DWT extension mode is set to periodization. For the other extension modes, SX = 2*size(cA)-lf+2.

For more information about the different Discrete Wavelet Transform extension modes, see dwtmode.

X = idwt2(cA,cH,cV,cD,'wname',S) and X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R,S) return the size-S central portion of the result obtained using the syntax idwt2(cA,cH,cV,cD,'wname'). S must be less than SX.

X = idwt2(...,'mode',MODE) computes the wavelet reconstruction using the extension mode MODE that you specify.

X = idwt2(cA,[],[],[],...) returns the single-level reconstructed approximation coefficients matrix X based on approximation coefficients matrix cA.

X = idwt2([],cH,[],[],...) returns the single-level reconstructed detail coefficients matrix X based on horizontal detail coefficients matrix cH.

The same result holds for X = idwt2([],[],cV,[],...) and
X = idwt2([],[],[],cD,...), based on vertical and diagonal details.

More generally, X = idwt2(AA,HH,VV,DD,...) returns the single-level reconstructed matrix X, where AA can be cA or [], and so on.

idwt2 is the inverse function of dwt2 in the sense that the abstract statement
idwt2(dwt2(X,'wname'),'wname') would give back X.

Remarks

If cA,cH,cV,cD are obtained from an indexed image analysis or a truecolor image analysis, they are m-by-n matrices or m-by-n-by-3 arrays, respectively.

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

Examples

• % The current extension mode is zero-padding (see dwtmode).
  
  % Load original image. 
  load woman;
  
  % X contains the loaded image. 
  sX = size(X);
  
  % Perform single-level decomposition 
  % of X using db4. 
  [cA1,cH1,cV1,cD1] = dwt2(X,'db4');
  
  % Invert directly decomposition of X 
  % using coefficients at level 1. 
  A0 = idwt2(cA1,cH1,cV1,cD1,'db4',sX);
  
  % Check for perfect reconstruction. 
  max(max(abs(X-A0)))
  ans =
      3.4176e-10
  

Algorithm

See Also
dwt2, dwtmode, upwlev2

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