Cone-beam reconstruction from general discrete vertex sets using Radon rebinning algorithms

Addresses image reconstruction in cone-beam tomography from an arbitrary discrete set of positions of the cone vertex. As a first step in the analysis of the problem, the authors define some measures of how close a discrete vertex set comes to satisfying Tuy´s condition (1983). Next, they propose 3 rebinning algorithms which use Grangeat´s formula (1991) and Marr´s algorithm (1980), and are capable of accurate reconstructions. The first algorithm is designed to accurately process cone-beam data finely sampled along a vertex path satisfying Tuy´s condition. The second algorithm applies to pair-complete vertex sets. The third algorithm is suited to process any discrete vertex set. The efficacy of the algorithms is illustrated with reconstructions from computer-simulated data using several vertex sets, including a set of randomly placed vertices