Volume integral model for algebraic image reconstruction and computed tomography

Industrial computed tomography (CT) has seen widespread adoption as an inspection technique due to its ability to resolve small defects and perform high-resolution measurements on complex structures. The reconstruction of CT data is usually performed using filtered back-projection (FBP) methods, such as the Feldkamp-Davis-Kress (FDK) method, and are selected as they offer a good compromise between reconstruction time and quality. More recently, iterative reconstruction algorithms have seen a resurgence in research interest as computing power has increased. Iterative reconstruction algorithms, such as the algebraic reconstruction technique (ART), use a reconstruction approach based on linear algebra to determine voxel attenuation coefficients based on the measured attenuation of the sample at the detector and calculation of the ray paths traversing the voxel grid. This offers a more precise model for CT reconstruction but at the cost of computational complexity and reconstruction time. Existing ART implementations are based on the 2D weighting models of the binary integral method (BIM), line integral method (LIM) and area integral method (AIM). For full 3D reconstruction, BIM and LIM only offer approximations leading to numerical inaccuracies. AIM for 2D reconstruction is mathematically exact but considers the divergent nature of a fan beam for 2D only. For a full 3D volumetric reconstruction, the X-ray cone beam is divergent in all directions and therefore AIM cannot be applied in its current form. A novel voxel weighting method for 3D volumetric image reconstruction using ART and providing a mathematically exact fractional volume weighting is introduced in this paper and referred to as the volume integral method (VIM). A set of algorithms is provided based on computer graphics techniques to determine ray/voxel intersections with volume reconstruction computed based on the divergence theorem. A set of experimental configurations is developed to provide a comparison against existing methods and conclusions are provided. Optimisation is achieved through graphic acceleration.