Cylindrical and spherical ray-tracing for CT iterative reconstruction

Recent events showed that dose administration has become a major concern regarding clinical computed tomography (CT) examinations. A simple solution to lower this dose is the use of more appropriate CT image reconstruction methods. Iterative reconstruction has not yet fully reached clinical applications, mostly due to computer speed and memory limitations. A method is proposed to compute a 3D system matrix using a polar-like voxel representation, allowing the modeling of highly resolved fields of view with a minimal random-access memory usage. As opposed to conventional ray-tracing, which is usually done over Cartesian coordinates, the proposed method uses cylindrical or spherical coordinates. The azimuthal symmetries present in those systems allow to compute only the detector responses of the first projection and use them as-is for all other projections. During reconstruction, only the azimuthal index has to be recomputed, and this is done using a simple addition. The ray-tracing and reconstruction algorithms were implemented and images of analytical phantoms were successfully reconstructed. Fully 3D images of phantoms and small animals acquired with a Gamma Medica Triumph X-O™ CT scanner are also presented to demonstrate the accuracy and robustness of the proposed approach. Under a reasonable set of assumptions, the memory size of the system matrix can be reduced by a factor corresponding to the number of projections. Using this strategy, iterative reconstruction from high resolution clinical and preclinical systems can be performed on general-purpose personal computers.