A filtered backprojection algorithm for cone beam reconstructionusing rotational filtering under helical source trajectory

With the evolution from multi‐detector‐row CT to cone beam (CB) volumetric CT, maintaining reconstruction accuracy becomes more challenging. To combat the severe artifacts caused by a large cone angle in CB volumetric CT, three‐dimensional reconstruction algorithms have to be utilized. In practice, filtered backprojection (FBP) reconstruction algorithms are more desirable due to their computational structure and image generation efficiency. One of the CB‐FBP reconstruction algorithms is the well‐known FDK algorithm that was originally derived for a circular x‐ray source trajectory by heuristically extending its two‐dimensional (2‐D) counterpart. Later on, a general CB‐FBP reconstruction algorithm was derived for noncircular, such as helical, source trajectories. It has been recognized that a filtering operation in the projection data along the tangential direction of a helical x‐ray source trajectory can significantly improve the reconstruction accuracy of helical CB volumetric CT. However, the tangential filtering encounters latitudinal data truncation, resulting in degraded noise characteristics or data manipulation inefficiency. A CB‐FBP reconstruction algorithm using one‐dimensional rotational filtering across detector rows (namely CB‐RFBP) is proposed in this paper. Although the proposed CB‐RFBP reconstruction algorithm is approximate, it approaches the reconstruction accuracy that can be achieved by exact helical CB‐FBP reconstruction algorithms for moderate cone angles. Unlike most exact CB‐FBP reconstruction algorithms in which the redundant data are usually discarded, the proposed CB‐RFBP reconstruction algorithm make use of all available projection data, resulting in significantly improved noise characteristics and dose efficiency. Moreover, the rotational filtering across detector rows not only survives the so‐called long object problem, but also avoids latitudinal data truncation existing in other helical CB‐FBP reconstruction algorithm in which a tangential filtering is carried out, providing better noise characteristics, dose efficiency and data manipulation efficiency.