%Basis vectors with coefficients:
f = @(x, y,a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4)...
a1*cos(0*x + 0*y) + a2*cos(0*x + 1*y) +...
a3*cos(0*x + 2*y) + a4*cos(0*x + 3*y) + ...
b1*cos(1*x + 0*y) + b2*cos(1*x + 1*y) + ...
b3*cos(1*x + 2*y) + b4*cos(1*x + 3*y) + ...
c1*cos(2*x + 1*y) + c2*cos(2*x + 1*y) + ...
c3*cos(2*x + 2*y) + c4*cos(3*x + 3*y) + ...
d1*cos(3*x + 1*y) + d2*cos(3*x + 1*y) + ...
d3*cos(3*x + 2*y) + d4*cos(3*x + 3*y)
%Matrix of image space:
[X,Y] = meshgrid(0:3);
%Creating the image from Fourier space by assigning coefficients:
F = f(X,Y,1,1,-1,1,1,1,1,6,3,1,1,1,7,1,1,1)

F =

   27.00000   -6.10793    5.54833  -12.13151
   -0.17799  -11.46000    6.76692    3.21717
    3.50819    6.10159    4.59486   -5.21914
  -18.13973    3.19193   -7.90075    6.77199


Fourier =

    5.5639 +  0.0000i    3.1811 +  0.9129i   36.8357 +  0.0000i    3.1811 -  0.9129i
    5.3234 - 14.4227i   33.6355 +  2.0031i   43.5672 - 50.8361i   11.4412 -  8.5912i
   41.0249 +  0.0000i   37.5489 - 35.6015i   79.1810 +  0.0000i   37.5489 + 35.6015i
    5.3234 + 14.4227i   11.4412 +  8.5912i   43.5672 + 50.8361i   33.6355 -  2.0031i