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

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

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:

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 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 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 filterfmod 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.