An exact reconstruction algorithm in variable pitch helical cone-beam CT when PI-line exists

In this paper, variable pitch helical cone-beam CT is studied. We prove a sufficient condition for the existence of PI-lines inside this variable pitch helix. Under this condition. we propose a new scanning configuration, called a spring scan, which can be used to scan a cylindrical object support. Based on Zou and Pan's BPF algorithm, we develop an exact BPF-type reconstruction algorithm for helical cone-beam CT in which the pitch of the helix varies with rotation angles. The algorithm includes four steps and can be used in region-of-interest (ROI) reconstruction by the PI-line determination step without a rebinning procedure as other BPF algorithms. Moreover, the algorithm can exactly reconstruct the object image only using the projection data within the Tam-Danielsson window, while; Katsevich's algorithm requires more data than it. Furthermore, we test the proposed algorithm using the 3D Shepp-Logan phantom by a spring scan. The numerical results are described to support the correctness of the algorithm.