Quasi-exact filtered backprojection algorithm for long-object problem in helical cone-beam tomography

Exact reconstruction from axially truncated cone-beam projections acquired with a helical vertex path is a challenging problem for which solutions are currently under investigation by some researchers. This paper deals with a difficult class of this problem called the long-object problem. Its purpose is to reconstruct a central region of interest (ROI) of a long object when the helical path extends only a little bit above and below the ROI. By extending the authors´ recent approach based on the triangular decomposition of the Grangeat formula, the authors derive quasi-exact reconstruction algorithms whose overall structure is of filtered backprojection (FBP) style. Unlike the previous similar approaches to the long-object problem, the proposed FBP algorithms do not require additional two circular scans at the ends of the helical path. Furthermore, the algorithms require a significantly smaller detector area and achieve improved image quality even for a large pitch compared with the approximate Feldkamp algorithms. One drawback of the proposed algorithms is the computational time, which is much longer than for the Feldkamp algorithms. The authors show some simulation results to demonstrate the performances of the proposed algorithms.