Grangeat-type half-scan algorithm for cone beam CT

Abstract

Currently, various cone-beam CT scanners are under rapid development for major biomedical applications. Half-scan cone-beam image reconstruction algorithms are desirable, which assume only part of a scanning turn, and are advantageous in terms of temporal resolution. While the existing half-scan cone-beam algorithms are in the Feldkamp framework, we formulate a half-scan algorithm in the Grangeat framework for circular and helical trajectories. First, we modify the Grangeat formula in the circular half-scan case. With analytically defined boundaries, the Radon space is partitioned into shadow zone, singly and doubly sampled regions, respectively. A smooth weighting scheme is designed to compensate for data redundancy and inconsistency. The sampled regions are linearly interpolated into the shadow zone for a complete data set. Then, these concepts and formulas are extended to the helical half-scan case. Extensive numerical simulation studies are performed to verify the correctness and demonstrate the performance. Our Grangeat-type half-scan algorithms allow minimization of redundant data and optimization of temporal resolution, and outperform Feldkamp-type reconstruction in terms of image artifacts. These algorithms seem promising for quantitative and dynamic biomedical applications of cone-beam tomography.