Tomographic Model Based Iterative Reconstruction of Symmetric Objects

Computed Tomography (CT) reconstruction of objects with cylindrical symmetry can be performed with a single projection. When the measured rays are parallel, and the axis of symmetry is perpendicular to the optical axis, the data can be modeled with the so-called Abel Transform. The Abel Transform has been extensively studied and many methods exist for accurate reconstruction. However, most CT geometries are cone-beam rather than parallel-beam. Using Abel methods for reconstruction in these cases can lead to distortions and reconstruction artifacts. Here, we develop analytic and model-based iterative reconstruction (MBIR) methods to reconstruct symmetric objects with an arbitrary axis of symmetry from a cone-beam geometry. The MBIR methods demonstrate superior results relative to the analytic inversion methods by mitigating artifacts and reducing noise while retaining fine image features. We demonstrate the efficacy of our methods using simulated and experimentally-acquired x-ray and neutron projections.