What's the frequency transform of a random matrix?
That is the DC offset (at zero frequency).

img = 255*randn(512);  % thanks @Jason's comment
img1=img-mean(img(:));
fftimg = abs(fft2(img1));
imagesc((fftshift(fftimg)))


gives you the spectrum of the normal distribution image. Note that white noise is flat in the frequency domain, but the Gaussian noise in the time domain is still Gaussian in the frequency domain. You may need to average a large number of FFTs of white noise to approach the average power spectral density.