Problem $3$: Remove Additive Cosine Noise $[15$ points$]$ The noisy image boy$\_$noisy.gif has been generated by adding some noise in the form of a cosine function. Your goal is to remove the cosine interference. This can be done as follows: a$)$ Compute the FT of the noisy image. $[2$ points$]$ b$)$ Compute the magnitude and find the frequencies corresponding to the four largest distinct magnitudes $($do not consider the magnitude at the center $$ a very large value$)[3$ points$]$ c$)$ Replace each one of these magnitude values by the average of its $8$ neighbors $($do this averaging both for the real and imaginary parts. Make sure you will perform this change for their symmetric points to ensure the proper reconstruction$).[5$ points$]$ d$)$ Take the inverse FT transform and display the original image and the resulted image side$-$byside in figure $1$ with the appropriate titles. $[2$ points$]$ e$)$ Explain why the four largest distinct values of the magnitude were chosen to do the processing via Matlab display command. $[3$ points$]$ f$)$ Close all figures and all variables in the workspace. Problem $3$: Remove Additive Cosine Noise $[15$ points$]$

The noisy image boy$\_$noisy.gif has been generated by adding some noise in the form of a cosine function.

Your goal is to remove the cosine interference. This can be done as follows:

a$)$ Compute the FT of the noisy image. $[2$ points$]$

b$)$ Compute the magnitude and find the frequencies corresponding to the four largest distinct magnitudes $($do not consider the magnitude at the center $-$ a very large value$)[3$ points$]$

c$)$ Replace each one of these magnitude values by the average of its $8$ neighbors $($do this averaging both for the real and imaginary parts. Make sure you will perform this change for their symmetric points to ensure the proper reconstruction$).[5$ points$]$

d$)$ Take the inverse FT transform and display the original image and the resulted image side$-$byside in figure $1$ with the appropriate titles. $[2$ points$]$

e$)$ Explain why the four largest distinct values of the magnitude were chosen to do the processing via Matlab display command. $[3$ points$]$

f$)$ Close all figures and all variables in the workspace.