Algebraic reconstruction techniques can be made computationally efficient [positron emission tomography application].

Algebraic reconstruction techniques (ART) are iterative procedures for recovering objects from their projections. It is claimed that by a careful adjustment of the order in which the collected data are accessed during the reconstruction procedure and of the so-called relaxation parameters that are to be chosen in an algebraic reconstruction technique, ART can produce high-quality reconstructions with excellent computational efficiency. This is demonstrated by an example based on a particular (but realistic) medical imaging task, showing that ART can match the performance of the standard expectation-maximization approach for maximizing likelihood (from the point of view of that particular medical task), but at an order of magnitude less computational cost.