## MATLAB exercise 2

### To be handed in on or
before Dec 13, 2010. Please hand in the answers to the questions and send the
MATLAB code that you used and the deconvolved images
by email to a.shulevski_at_astro.rug.nl.

1. Read in the image escher_waterfall.jpg

2. Blur this image in MATLAB with a Gaussian
filter with dispersion of 4 pixels. Use the function *fspecial*
in Matlab. Now add noise to the image using normally
distributed random numbers with a standard deviation of 2.

Wiener filtering is a technique that uses the blurring function (the impulse response)
and restores the images the information at each frequency in a way that depends
on the Signal to Noise ratio at that frequency. See e.g. Wikipedia, and
also here, for more
information.

3. Now use the implementation of the Wiener deconvolution
in Matlab (the program *deconvwnr*)
to restore the original image as much as possible. You are allowed to use all
the options in the program.

We will now deconvolve the image using 2 methods: the
method of Van Cittert, and Richardson-Lucy deconvolution. Read the document about these deconvolution methods that is given below.

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4. Use Van Cittert deconvolution with w(p)=1 to deconvolve the image. With how many
iterations do you get the best result? Now use a sine function. With
which value ofdo you get the best results and in how many iterations?

5. Do the same using Richardson-Lucy deconvolution, also using a sine function as a weight
function. With which value ofdo you get the best results and in how many iterations?

6. Now discuss quantitatively which of the 3
methods is better. Which method gives the best reconstruction? How do you
measure this? Which method preserves the low frequencies best? And the high frequencies?

7. For an additional exercise in understanding Fourier
Transforms see Problem_set_2a