Gordon ART

Algorithm contributed by Gordon et al. [97] is considered. Mayinger’s ART is similar to this original version under the condition that no two ray simultaneously pass through a particular cell for a given projection. In this method corrections are applied to all the cells through which the -th passes, using the weight factor which is exactly the proportion of to the total length of the ray. The projection data gets updated after calculations through each ray. This procedure will be referred to as ART2. The individual steps are:

Calculate the total value of weight function along each ray as:

Start:1 For each projection angle
Start:2 For each ray
Start:3 For each cell

Close:3
Close:2
Close:1
Start:4 start iterations
Start:5 For each projection angle
Start:6 For each ray

Compute the numerical projection (Eqution 22)
Calculate the correction as:

Start:7 For each cell
If is non-zero then:

where  is a relaxation factor:
Close:7
Close:6
Close:5
Check for convergence as:
If

STOP:
Else: Continue
Close: 4