We'll use the scipy.fftpack module's fft2()/ifft2() function to compute the DFT/IDFT with the FFT algorithm using a grayscale image, rhino.jpg:

im = np.array(Image.open('../images/rhino.jpg').convert('L')) # we shall work with grayscale image
snr = signaltonoise(im, axis=None)
print('SNR for the original image = ' + str(snr))
# SNR for the original image = 2.023722773801701
# now call FFT and IFFT
freq = fp.fft2(im)
im1 = fp.ifft2(freq).real
snr = signaltonoise(im1, axis=None)
print('SNR for the image obtained after reconstruction = ' + str(snr))
# SNR for the image obtained after reconstruction = 2.0237227738013224
assert(np.allclose(im, im1)) # make sure the forward and inverse FFT are close to each other
pylab.figure(figsize=(20,10))
pylab.subplot(121), pylab.imshow(im, cmap='gray'), pylab.axis('off')
pylab.title('Original Image', size=20)
pylab.subplot(122), pylab.imshow(im1, cmap='gray'), pylab.axis('off')
pylab.title('Image obtained after reconstruction', size=20)
pylab.show()

Here's the output: 

As can be seen from the SNR values from the inline output and from the visual difference in the input and the reconstructed image, the reconstructed image loses some information. The difference is negligible if we use all of the coefficients obtained for reconstruction