Error analysis on a generalized Feldkamp's cone‐beam computed tomography algorithm

To overcome the limitations of Feldkamp's cone‐beam reconstruction algorithm, we generalized it in the case of noncircular and nonplanar scanning. In this paper, an error analysis is performed on this generalized approximate algorithm. The study is based on a reconstruction error formula. Roughly speaking, the error is proportional to the distance from a voxel to the mid‐plane in the planar scanning mode, to the pitch of a scanning locus in the helix‐like scanning mode, and inversely proportional to the horizontal size of the scanning locus. The error also depends on longitudinal variation of a specimen function. Longitudinal partial derivative distributions of specimen transverse sections are modeled as stochastic fields. Practical factors are simulated as noise terms in the reconstruction error formula. The simulation results show that the generalized Feldkamp's algorithm is not sensitive to noise and allows more accurate reconstruction in the helix‐like scanning mode.