How this decomposition must be done? should I use ICA?

Consider we have these 3 image frames:

if true
  A = [ 1 1 0 0 0 0 
        1 1 0 0 0 0
        1 1 0 0 0 0
        1 1 0 0 0 0
        1 1 0 0 0 0
        1 1 0 0 0 0 ]

B =   [ 1 1 1 1 1 1
        1 1 1 1 1 1
        0 0 0 0 0 0 
        0 0 0 0 0 0 
        0 0 0 0 0 0
        0 0 0 0 0 0 ]

   C = [ 0 0 0 0 0 0
         0 0 0 0 0 1
         0 0 0 0 1 1       
         0 0 0 1 1 1
         0 0 1 1 1 1
         0 1 1 1 1 1 ]
end

Each of these frames is consisted of only one edge(1 vertical, 1 horizontal and 1 diagonal). Now imagine we have:

D = A + B + C;

We know the matrix D is the sum of some "1-edge" image frames(we do not know how many) and we want to decompose D into those frames. What image processing technic must be used? Should I use ICA? If so would you please give me some hints on how to run ICA on a matrix to achieve this kind of components?

Or do you think it is more convenient to work on their DFTs? since:

fft(D) = fft(A) + fft(B) + fft(C);

and we know that for each edge we will get 1 set of harmonic frequencies perpendicular to the edge (and for diagonal edges one or 2 more sets in other directions). Can we run ICA on real and imaginary part of the DFT of the image?

THANK YOU ALL

payman