Figure 30. The Algebraic Reconstruction Technique.

ART is based on the fact that projection values are integrals of the spectrum along lines. The spectrum is divided into discrete elements, here 2-D pixels numbered S(x, y). For an individual observed projection value, such as point A at left, one can write a linear equation describing the projection intensity as the sum of weighted contributions from the pixels of the spectrum. To determine the weight for a specific pixel on a specific projection point, one extends vectors from the projection across the spectrum (dashed lines) and determines the overlap integral. For example, the weight of pixel S(2, 2) on the orange projection point is determined by the area of the region U, while that of S(3, 3) on point B is determined by the area of region V. After defining this system of linear equations, ART proceeds by adjusting the values of S iteratively until the calculated sums agree with the observed data.