An approximate analytical reconstruction method in inverse problems of Cone-beam Rotary Computed Laminography

Abstract Computed tomography is a highly effective inspection methodology for non-destructive testing, however, it faces challenges with objects that have a significant aspect ratio. In such scenarios, computed laminography (CL) serves as a viable alternative. The unique geometric configuration of cone-beam rotary CL makes the classical FDK reconstruction algorithm unsuitable. To address this inverse problem, we proposed an approximate analytical reconstruction method inspired by the core idea of the FDK algorithm. Firstly, we addressed the cone-beam rotary CL reconstruction problem by approximating it as a series of fan-beam reconstruction tasks, and deriving the geometric relationships between the original coordinate system and the fan-beam coordinates. Secondly, the fan-beam reconstruction formula within the fan-beam coordinate system is derived. Finally, disregarding the fact that the projection data come from different planes based on the idea of the Feldkamp–Davis–Kress algorithm, an approximate analytical reconstruction algorithm is derived based on the geometric relationships between the original coordinate system and the detector coordinates. The effectiveness of our method is demonstrated through simulations and real data experiments. The results demonstrate that the proposed method mitigates the superimposition artifacts and enhances the fine structural details to a certain extent compared to the CL-filtered backprojection method, while preserving the object boundaries.