CONE-BEAM RECONSTRUCTION BY THE USE OF RADON-TRANSFORM INTERMEDIATE FUNCTIONS

A mathematical framework is presented for cone-beam reconstruction by intermediate functions that are related to the three-dimensional Radon transform of the object being imaged. Cone-beam projection data are processed with a filter to form an intermediate function. The filter is a linear combination ah(1)(l) + bh(2)(l) of the ramp kernel hill) and the derivative functional hz(l). From the intermediate function, the reconstruction is completed with a convolution and backprojection, where the convolution filter is another linear combination ch(1)(l) + dh(2)(l) subject to the restriction ac + bd = 1. This formulation unifies and generalizes the important cone-beam formulas of Tuy [SIAM J. Appl. Math. 43, 546 (1983)], Smith [IEEE Trans. Med. Imaging MI-4, 14 (1985)], and Grangeat [Ph.D. dissertation (Ecole Nationale Superieure des Telecommunications, Paris, 1987)]. The appropriate values of a, b, c, d for these methods are derived.