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Noise and Fourier Transforms

30 min.
At the end of this practical you should be able to:
- understand the concept of image noise
- The concept of the fourier transform


Digital Images
Grey Levels
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 Processing Toolbox. (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 image?
- 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 component).

(c) Imaging Science and Biomedical Engineering 2000 [paul.bromiley@man.ac.uk]

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