Convolution reconstruction techniques for divergent beams

A rigorous derivation of a convolution reconstruction technique for diverging beams which does not require reordering the data is given. It is shown that such techniques allow both rapid data collection and rapid but nevertheless accurate reconstruction. The performance of the method is demonstrated by reconstructions of both a mathematically generated phantom representing cross sections of the human thorax and also cross sections of the intact thorax of a dog from actual X-ray data.