Implementation of Tuy's cone-beam inversion formula

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Abstract
Tuy's cone-beam inversion formula (see SIAM J. appl. math., vol.43, p.546-52, 1983) was modified to develop a cone-beam reconstruction algorithm. The algorithm was implemented for a cone-beam vertex orbit consisting of a circle and two orthogonal lines. This orbit geometry satisfies the cone-beam data sufficiency condition and is easy to implement on commercial single photon emission computed tomography (SPECT) systems. The algorithm, which consists of two derivative steps, one rebinning step, and one three-dimensional backprojection step, was verified by computer simulations and by reconstructing physical phantom data collected on a clinical SPECT system. The proposed algorithm gives equivalent results and is as efficient as other analytical cone-beam reconstruction algorithms.