Reconstruction-plane-dependent weighted FDK algorithm for cone beam volumetric CT

Abstract

The original FDK algorithm has been extensively employed in medical and industrial imaging applications. With an increased cone angle, cone beam (CB) artifacts in images reconstructed by the original FDK algorithm deteriorate, since the circular trajectory does not satisfy the so-called data sufficiency condition (DSC). A few “circular plus” trajectories have been proposed in the past to reduce CB artifacts by meeting the DSC. However, the circular trajectory has distinct advantages over other scanning trajectories in practical CT imaging, such as cardiac, vascular and perfusion applications. In addition to looking into the DSC, another insight into the CB artifacts of the original FDK algorithm is the inconsistency between conjugate rays that are 180° apart in view angle. The inconsistence between conjugate rays is pixel dependent, i.e., it varies dramatically over pixels within the image plane to be reconstructed. However, the original FDK algorithm treats all conjugate rays equally, resulting in CB artifacts that can be avoided if appropriate view weighting strategy is exercised. In this paper, a modified FDK algorithm is proposed, along with an experimental evaluation and verification, in which the helical body phantom and a humanoid head phantom scanned by a volumetric CT (64 x 0.625 mm) are utilized. Without extra trajectories supplemental to the circular trajectory, the modified FDK algorithm applies reconstruction-plane-dependent view weighting on projection data before 3D backprojection, which reduces the inconsistency between conjugate rays by suppressing the contribution of one of the conjugate rays with a larger cone angle. Both computer-simulated and real phantom studies show that, up to a moderate cone angle, the CB artifacts can be substantially suppressed by the modified FDK algorithm, while advantages of the original FDK algorithm, such as the filtered backprojection algorithm structure, 1D ramp filtering, and data manipulation efficiency, can be maintained.