Consider the simple $48,8-$bit image:

$($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$)$ Consider Huffman encoding pairs of pixels rather than individual pixels.

That is$,$ consider the image to be produced by the second extension of the

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 en$-$

tropy of the new difference image? What does this tell us about compressing

the image?

$($f$)$ Explain the entropy differences in $($a$),($d$)$ and $($e$).$