Getting the contrast from DFT

Hello Experts,

Given the spectrum image:

F(u,v) = (1/N^2) * Sum(from x=0 to N-1)Sum(from y = 0 to N-1) [f(x,y) * exp(-i* (2*pi/N)*(u*x + v*y))]

I need to find using Parseval equation: Double Sum x=0..N-1,y=0..N-1 [f^2(x,y)] = (1/N^2) * Double Sum v=0..N-1, u=0..N-1 [F^2(u,v)].

That I can get c^2 = (1/N^2)* Double Sum v=0..N-1, u=0..N-1 [f(x,y) - B]^2

Where B = 1/N^2 Double Sum x=0..N-1, y = 0..N-1 [f(x,y)] = F(0,0)

This is all part of image processing, B is brightness, c is contrast.

Please help me to get the contrast from the spectrum image.

Thanks a lot in advance. Or maybe you know where can I see the proof.