% idct2.m
% inverse discrete cosine transform in 2d
% (painfully slow)

function f = idct2(F)

[m,n] = size(F);
f = zeros(m,n);

% transform rows
k=[0:n-1]*pi/n/2;
w=[sqrt(0.5), ones(1,n-1)]*sqrt(2/n);
for ml=1:m
   for nl=1:n
      f(ml,nl) = sum( w .* F(ml,:) .* cos(k.*(2*nl-1)) );
   end
end

% transform columns
F=f;
k=[0:m-1]'*pi/m/2;
w=[sqrt(0.5); ones(m-1,1)]*sqrt(2/m);
for nl=1:n
   for ml=1:m
      f(ml,nl) = sum( w .* F(:,nl) .* cos(k.*(2*ml-1)) );
   end
end