Part $1$: Image Restoration by Wiener Filter

Write a MATLAB function Wiener$\_$filter that performs the parametric Wiener filtering restoration in the

frequency domain. The function takes as input the degraded image $g(x,y),$ and returns the estimated image

$f(x,y)$ after Wiener filtering. The Wiener filter is given in the Eq$.(5\mathrm{.}8-6)$ shown below.

hat$(F)(u,v)=[\frac{1}{H(u,v)}\frac{|H(u,v){|}^2}{|H(u,v){|}^2+K}]G(u,v)$

Note: Try several K to obtain a least MSE, the mean square error MSE between the original and

restored images can be computed by using the Eq$.(5\mathrm{.}8-4)$ shown below:

MSE $=\frac{1}{MN}{\displaystyle \underset{x=0}{\overset{M-1}{}}}{\displaystyle \underset{y=0}{\overset{N-1}{}}}[f(x,y)-$hat$(f)(x,y){]}^2$

Where $f(x,y)$ is the original image

Use your function Wiener$\_$filter to restore the degradeCameraMan.tif given in the Model course page.

Also, you are giving the original image CameraMan.tif in the Moodle course page that you will use to

compute the MSE.

The degradation function $H(u,v)$ that will use it for Wiener restoration is

$1-$ The motion blurring degradation function giving by the Eq$.(5\mathrm{.}6-11)$ shown below, where $a=b=0\mathrm{.}1$

and $T=1$ :

$H(u,v)=\frac{T}{(ua+vb)}sin[(ua+vb)]e^{-j(ua+vb)}$

$2-$ The Atmospheric Turbulence filter giving by Eq$.(5\mathrm{.}6-3)$ shown below where $k=0\mathrm{.}001$ :

$H(u,v)=e^{-k(u^2+v^2{)}^{\frac{5}{6}}}$

Discuss how well the Wiener filtering restored the original image in both cases i$.$e$.$ when motion blurring

degradation function is used and when atmospheric turbulence filter is use and which one is better.