A tutorial on art (algebraic reconstruction techniques)

Algebraic reconstruction techniques (ART) were introduced by Gordon et al. (1970) for solving the problem of three dimensional reconstruction from projections in electron microscopy and radiology. An X-ray photograph represents the projection of the three-dimensional distribution of X-ray densities within the body onto a two-dimensional plane. A finite number of such photographs taken at different angles allows one to reconstruct an estimate of the original 3-D densities. The ART algorithms for solving this problem have a simple intuitive basis. Each projected density is thrown back across the higher dimensional region from whence it came, with repeated corrections to bring each projection of the estimate into agreement with the corresponding measured projection.