Tomography for a $33$ image. You are given exact measurements of the row and column sums of

the pixels $(6$ measurements$).$

$($a$)$ Can you recover the image? How? Why?

$($b$)$ "Ghosts" are images that produce exactly zero measurements. Write a matlab program to generate

random ghosts. Show three of these ghosts. How are the ghosts related to your ability or inability

to reconstruct the image?

$($c$)$ You suspect that your assistant was too lazy to collect actual measurements, and just fabricated

the numbers instead. Construct a certain projector and show how use it to verify your suspicion.

$($d$)$ Repeat $($a$)-($c$)$ when you are also given the sums along the two main diagonals and two subdiag$-$

onals in each direction $($total of $6+2+4=12$ measurements$).$

$($e$)$ Would your answers to $($a$)-($c$)$ change if you knew the image is non$-$negative? How?