Wavelet Toolbox

lwtcoef2

Extract or reconstruct 2-D LWT wavelet coefficients

Syntax

• Y = lwtcoef2(TYPE,XDEC,LS,LEVEL,LEVEXT)
  Y = lwtcoef2(TYPE,XDEC,W,LEVEL,LEVEXT)
  

Description

Y = lwtcoef2(TYPE,XDEC,LS,LEVEL,LEVEXT) returns the coefficients or the reconstructed coefficients of level LEVEXT, extracted from XDEC, the LWT decomposition at level LEVEL obtained with the lifting scheme LS.

The valid values for TYPE are

TYPE Values	Description
'a'	approximations
'h'	horizontal details
'v'	vertical details
'd'	diagonal details
'ca'	coefficients of approximations
'ch'	coefficients of horizontal details
'cv'	coefficients of vertical details
'cd'	coefficients of diagonal details

Y = lwtcoef2(TYPE,XDEC,W,LEVEL,LEVEXT) returns the same output using W, which is the name of a lifted wavelet.

Examples

• % Start from the Haar wavelet and get the
  % corresponding lifting scheme.
  lshaar = liftwave('haar');
  
  % Add a primal ELS to the lifting scheme.
  els = {'p',[-0.125 0.125],0};
  lsnew = addlift(lshaar,els);
  
  % Perform LWT at level 2 of a simple image.
  x = reshape(1:16,4,4);
  xDec = lwt2(x,lsnew,2)
  
  xDec =
  
     27.4375    4.0000   17.0000    4.0000
      1.0000         0    1.0000         0
      4.2500    4.0000    0.0000    4.0000
      1.0000         0    1.0000         0
  
  % Extract approximation coefficients of level 1.
  ca1 = lwtcoef2('ca',xDec,lsnew,2,1)
  
  ca1 =
  
      5.7500   22.7500
     10.0000   27.0000
  
  % Reconstruct approximations and details.
  a1 = lwtcoef2('a',xDec,lsnew,2,1)
  
  a1 =
  
      2.8750    2.8750   11.3750   11.3750
      2.8750    2.8750   11.3750   11.3750
      5.0000    5.0000   13.5000   13.5000
      5.0000    5.0000   13.5000   13.5000
  
  a2 = lwtcoef2('a',xDec,lsnew,2,2)
  
  a2 =
  
      6.8594    6.8594    6.8594    6.8594
      6.8594    6.8594    6.8594    6.8594
      6.8594    6.8594    6.8594    6.8594
      6.8594    6.8594    6.8594    6.8594
  
  h1 = lwtcoef2('h',xDec,lsnew,2,1)
  
  h1 =
  
     -0.3750   -0.3750   -0.3750   -0.3750
      0.6250    0.6250    0.6250    0.6250
     -0.5000   -0.5000   -0.5000   -0.5000
      0.5000    0.5000    0.5000    0.5000
  
  v1 = lwtcoef2('v',xDec,lsnew,2,1)
  
  v1 =
  
     -1.5000    2.5000   -2.0000    2.0000
     -1.5000    2.5000   -2.0000    2.0000
     -1.5000    2.5000   -2.0000    2.0000
     -1.5000    2.5000   -2.0000    2.0000
  
  d1 = lwtcoef2('d',xDec,lsnew,2,1)
  
  d1 =
  
       0     0     0     0
       0     0     0     0
       0     0     0     0
       0     0     0     0
  
  h2 = lwtcoef2('h',xDec,lsnew,2,2)
  
  h2 =
  
     -0.7969   -0.7969   -0.7969   -0.7969
     -0.7969   -0.7969   -0.7969   -0.7969
      1.3281    1.3281    1.3281    1.3281
      1.3281    1.3281    1.3281    1.3281
  
  v2 = lwtcoef2('v',xDec,lsnew,2,2)
  
  v2 =
  
     -3.1875   -3.1875    5.3125    5.3125
     -3.1875   -3.1875    5.3125    5.3125
     -3.1875   -3.1875    5.3125    5.3125
     -3.1875   -3.1875    5.3125    5.3125
  
  d2 = lwtcoef2('d',xDec,lsnew,2,2)
  
  d2 =
  
    1.0e-015 *
  
      0.2498    0.2498   -0.4163   -0.4163
      0.2498    0.2498   -0.4163   -0.4163
     -0.4163   -0.4163    0.6939    0.6939
     -0.4163   -0.4163    0.6939    0.6939
  
  % Check perfect reconstruction.
  err = max(max(abs(x-a2-h2-v2-d2-h1-v1-d1)))
  
  err =
  
    3.5527e-015
  

See Also

ilwt2, lwt2

lwtcoef

mexihat

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