Gilbert ART

Gilbert [98] has developed independently a form ART known as SIRT (Simultaneous Iterative Reconstruction Algorithm). In SIRT, the elements of the field function are modified after all the corrections corresponding to individual pixels have been calculated. This will be referred to as ART3. The numerically generated projection is computed once for all the angles and gets updated only after the completion of calculations through all the rays. For each ray from all angles, all the cells are examined to look for those rays which pass through a particular cell. For each cell, the rays which pass through it will contribute a correction that is decided by the weight factor . The algebraic average of all these corrections is implemented on the cell. This procedure will be called ART3. Its 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 (Eqution21)
Calculate the correction as:

Close: 6
Close: 5
Start:7 For each cell

Identify all the rays passing through given cell (j)let be the total number of rays passing through the th cell)and corresponding   and 

Apply correction as:

Where is relaxation factor.
Close: 7
Cheek for convergence as:
If

STOP:
Else:

close: 4