integral_op.m

采用matlab编写的数字图像恢复程序

  function Ku = integral_op(u,k_hat)
%
%  Ku = integral_op(u,k_hat)
%
%  Use 2-D FFT's to evaluate discrete approximation to the 
%  2-D convolution integral
%
%    Ku(x,y) = \int \int k(x-x',y-y') u(x',y') dx' dy'.
%
%  k_hat is the shifted 2-D discrete Fourier transform of the 2_D 
%  kernel evaluated at node points (x_i,y_j), and then extended.
%  u is also assumed to be evaluated at node points (x_i,y_j).
%  The size of k_hat is 4 times that of u, due to extension.

   n = max(size(u));
   h = 1 / n;
   n2 = 2 * n;
   Ku_ext = real(ifft2( ((fft2(u,n2,n2)) .* k_hat))) ;
   Ku = Ku_ext(1:n,1:n) * h^2;