Construct the FFT of the image and see if you can
relate it's main features back to the original image.
You can do this using fft2(x) from MATLABs Image
(you may have to view only
real or imaginary (real(x), imag(x)) components or select
a region of interest in order to see any structure).
Use "randn(256);" to generate uniform random noise
on each pixel.
After an initial trial to determine a suitable sequence
of processes, design a systematic set of tests to
investigate the behaviour of the real and imaginary
components of the FFT of the image for various
additive noise levels. You can measure the noise
directly by investigating the result of subtracting
the FFT of the original image. (if you have problems
with the resulting image being completely black or white
try removing the mean value of the image before the FFT)
Attempt to find answers to the following questions:
- Do you see any correlation between the level of
added noise and the noise in the Fourier domain?
- Do your results depend on the data in the original
- Given that you know how much noise there is in the
noisy FFT image can you find a way of estimating this
without subtracting the original image?
- If you were to apply a filter to a Fourier domain
image (as described by the convolution theorem) what
would be the consequences in terms of the noise on
the inverse? (Start by thinking about one sinusoidal