Question $4$

$($a$)$ In Computed Tomography $($CT$),$ image can be reconstructed using the backprojection approach. For any $\backslash (2\backslash$times $2\backslash )$ matrix $($refer to Table Q$4($a$)),$ answer the following questions.

Table $04($a$)$

$($i$)$ Appraise the summation matrix of all $4$ scans by pixels.

$(3$ marks$)$

$($ii$)$ Demonstrate mathematically that the normalization value, $\backslash (\backslash$mathrm$\{$n$\}=3\backslash ).$

$(8$ marks$)$

$($iii$)$ Proof that the background value, bg$,$ can be found by summing all pixels in the original matrix, or by dividing the sum of all pixels in the summation matrix in Q$4($a$)($i$)$ by $7.$

$(8$ marks$)$