ADJWINDOWONPPGRID

Adjoint W operator, adjoint subband windowing with 2D FFT

Contents

Description

Y = ADJWINDOWONPPGRID(Y,N,R,BETA)
  x: array (2,(R*n)+1,n+1) : (sector,radial,slope) 2 sectors.
  beta: 2 or 4; scaling factor 2^j or 4^j.
  R: oversampling rate
  y: digital shearlet coefficients which is a cell array:
     each y{sector,scale,tile} is a complex-valued matrix, 2D FFT
  sector runs through 4 values
  scale  runs through J     approx log(N)/log(beta/2) values
  tile   runs through Ntile approx beta^scale values   [OUCH!]

Examples

    R    = 4; beta = 4;
    img  = imread('barbara.gif');
    img  = double(img);
    N    = size(img,1);
    pimg = ppFT(img,R);
    shX  = WindowOnPPGrid(pimg,beta,0);
    size(shX)
    tpimg= AdjWindowOnPPGrid(shX,N,R,beta);
    size(tpimg)
    norm(squeeze(tpimg(1,:,:)-pimg(1,:,:)),inf)
    norm(squeeze(tpimg(2,:,:)-pimg(2,:,:)),inf)
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!

ans =

     4     8    65

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!

ans =

           2        2049         513


ans =

  2.0511e-009


ans =

  1.4006e-009

See also

MEYER, BUMPV, NV, PARASCALE, WINDOWONPPGRID.

Copyright

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