In practice, the linear independence condition implies that (1) the angle between any two projections must be greater than a critical minimum (which means that the projections must be equally distributed in the 180° angular range), and (2) the ray width (w) and the cell width (d) must have the same order of magnitude, i.e.

Since and ≈
condition (3-4) is equivalent to ≈ and therefore n ≈ r
This means that the requirement p·r = n² becomes p·n ≈ n² , which amounts to

The result, in conclusion, is that the minimum number of projections which are required for reconstructing a structure of n² unknowns is comparable to the square root of the number of the unknowns.
It is important to notice that, in real life applications, the actual number of projections must always be greater (often much greater) than the theoretical minimum, because of the need to compensate the inevitable loss of information which is produced by various types of noise.
It is also important to notice that the theoretical minimum obtained with non-algebraic methods (Crowther et al., 1970) is never inferior to the algebraic minimum. Expression (3-5), in other words, is the lowest possible estimate of the minimum number of projections that are required for a complete reconstruction of any given structure.

ART: an iterative algebraic method

The first algebraic reconstruction method was described by Hounsfield in 1969 in a patent application for computerized tomography, and an equivalent version was published independently by Gordon, Bender and Herman in 1970 with the name of ART (Algebraic Reconstruction Technique).