Abstract: In this paper, we consider 3D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays. All contemporary density reconstruction methods in high-energy X-ray radiography are based on the assumption that the cone beam can be treated as fan beams located at parallel planes perpendicular to the symmetric axis, so that the density of the whole object can be recovered layer by layer. Considering the relationship between different layers, we undertake the cone-beam global reconstruction to solve the ambiguity effect at the material interfaces of the reconstruction results. In view of the anisotropy of classical discrete total variations, a new discretization of total variation which yields sharp edges and has better isotropy is introduced in our reconstruction model. Furthermore, considering that the object density consists of continually changing parts and jumps, a high-order regularization term is introduced. The final hybrid regularization model is solved using the alternating proximal gradient method, which was recently applied in image processing. Density reconstruction results are presented for simulated radiographs, which shows that the proposed method has led to an improvement in terms of the preservation of edge location.

Key words: high-energy X-ray radiography, cone-beam global reconstruction, inverse problem, total variation, alternating proximal gradient method