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

Abstract

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).

Recent Advances in CT Image Reconstruction

“…Several modified trajectories, such as circle-plus-arc, circle-plus-line, dualcircle, or saddle trajectories ( Fig. 6; [21][22][23][24][25][26][27][28]) try to resolve the first problem listed above (missing frequency data). In , a phantom known to demonstrate such a problem is shown for just a single-circle trajectory on the left and a dual-circle trajectory on the right.…”

Experimental Study of Intracranial Hematoma Detection with Flat Panel Detector C-Arm CT

“…Unfortunately, a single partial-circle (or even full circle) scan in the cone-beam geometry provides inherently incomplete data for reconstructing sections off the midplane of the acquired volume, leading to streaking and shading that increases in severity as the plane of interest moves away from the midplane of the acquisition. [33][34][35][36][37] Note, however, that the brain of the swine is relatively small in the z-direction, so evidence of cone-beam artifact was not seen in this study.…”

3D Interventional Imaging with 2D X-Ray Detectors

“…This can produce pre-operative 3D images for planning but also interventionnal 3D images for controling. Since the beginning of 1980s, 3D reconstruction techniques from conical x-ray projections have been greatly improved [7,11,5,14]. Reconstructions of high contrast structures from few projections acquired on image intensifiers have been proposed [15,4].…”