A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection

An exact inversion formula written in the form of shift-variant filtered-backprojection (FBP) is given for reconstruction from cone-beam data taken from any orbit satisfying H.K. Tuy's (1983) sufficiency conditions. The method is based on a result of P. Grangeat (1987), involving the derivative of the three-dimensional (3D) Radon transform, but unlike Grangeat's algorithm, no 3D rebinning step is required. Data redundancy, which occurs when several cone-beam projections supply the same values in the Radon domain, is handled using an elegant weighting function and without discarding data. The algorithm is expressed in a convenient cone-beam detector reference frame, and a specific example for the case of a dual orthogonal circular orbit is presented. When the method is applied to a single circular orbit (even though Tuy's condition is not satisfied), it is shown to be equivalent to the well-known algorithm of L.A. Feldkamp et al. (1984).