AdjShearletTransform

Adjoint of Shearlet Transform. (W sqrt(w) P)^\star

Contents

Description

X=ADJSHEARLETTRANSFORM(SHX,N,R,BETA,W)
Input:
 ShX - shearlet coefficient structure from SHEARLETTRANSFORM
 N   - original image size N.
 R   - oversampling rate
 w   - weighting matrix, see GENERATEW
Output:
 X   - image of size N-by-N.

Examples

  tic
  img = imread('barbara.gif');
  img = double(img);
  N   = size(img,1); beta = 4;
  R   = 4; basisChoice  = 5;
  w   = generateW(N,R,basisChoice);
  shX = ShearletTransform(img, R, beta, w, 0);
  timg= AdjShearletTransform(shX,N,R,beta,w);
  err = norm(timg-img,'fro')/norm(img,'fro')
  toc

Forward Shearlet Transform...
ppFT ...
Weighting ...
Windowing ...
Decomposition of high-frequency part...
scale = 5, Number of Tiles = 65
scale = 4, Number of Tiles = 33
scale = 3, Number of Tiles = 17
scale = 2, Number of Tiles = 9
scale = 1, Number of Tiles = 5
scale = 0, Number of Tiles = 3
scale = -1, Number of Tiles = 1
Decomposition of low frequency part...
Done!
Done with Forward Shearlet Transform!
Backward Shearlet Transform...
Adjoint Windowing...
Reconstruction from high-frequency part...
scale = 5, Number of Tiles = 65
scale = 4, Number of Tiles = 33
scale = 3, Number of Tiles = 17
scale = 2, Number of Tiles = 9
scale = 1, Number of Tiles = 5
scale = 0, Number of Tiles = 3
scale = -1, Number of Tiles = 1
Reconstrucion from low frequency part...
Done!
Weighting...
AdjppFT...
Done with Backward Shearlet Transform!

err =

    0.0014

Elapsed time is 6.605784 seconds.

See also

INVSHEARLETTRANSFORM, SHEARLETTRANSFORM, PPFT, ADJPPFT, INVPPFTCG, WINDOWONPPGRID ADJWINDOWONPPGRID GENERATEW

Copyright

Copyright (C) 2011. Xiaosheng Zhuang, University of Osnabrueck

Published with MATLAB® 7.10