INVSHEARLETTRANSFORM

Inverse of Shearlet Transform using CG.

Contents

Description

X=INVSHEARLETTRANSFORM(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

 err - error controlled in CG

 itsMax- maximal iteration in CG

Output:

 X   - image of size N-by-N.

 it  - total iteration times in CG

 res - final iteration error in CG iteration

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')
  [timg, its, rerr] = InvShearletTransform(shX,N,R,beta,w,1e-5,3);
  err = norm(timg-img,'fro')/norm(img,'fro')
  its, rerr
  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

Inverse 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...
InvppFTCG...
Done with InverseShearlet Transform!

err =

  1.3143e-006


its =

     3


rerr =

    0.0046

Elapsed time is 18.598188 seconds.

See also

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

Copyright

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

Published with MATLAB® 7.10