Question $1[30$ pt$]$

$($a$)$: Compute the entropy of the image $($b$)$: Compress the image using Huffman coding $($c$)$: Compute the compression achieved

and the effectiveness of the Huffman coding $($d$)$: Coding Huffman pairs of pixels rather than individual pixels. That is$,$ consider

the image to be produced the original image. What is the entropy zero$-$memory source that produced the original image. What

is the entropy of the image when looked at as pairs of pixels? $($e$)$: Consider coding the differences between adjacent pixels.

What is the entropy of the new difference image? What does this tell us about compressing the image? $($f$)$: Explain the entropy

differences in $($a$),($d$)$ and $($e$)$