Three-term exact FBP reconstruction in cone-beam helical CT

Recently, Katsevich proposed an exact FBP algorithm and its improved version for image reconstruction in helical cone-beam CT. In this work, by modifying this algorithm, we derive a new algorithm for exact image reconstruction from helical cone-beam data. This new algorithm is easier to implement and more efficient than the improved version of Katsevich's algorithm, which contains five terms. The derived algorithm consists of three terms, and the two dominant terms can be obtained by computing the partial derivatives with respect to the coordinates on the detector plane. The third term remains a derivative along the helical trajectory, its contribution to the final reconstruction, however, is much smaller than that of the other two terms for practical scanning configurations. We performed computer-simulation studies to evaluate the performance of the proposed and Katsevich's algorithms. The numerical results of these studies confirm our theoretical predictions.