Fully 3D iterative CT reconstruction using polar coordinates

This paper demonstrates the feasibility of fully 3D iterative computed tomography reconstruction of highly resolved fields of view using polar coordinates.

System matrix is computed using a ray-tracing approach in cylindrical or spherical coordinates. By using polar symmetries inherent to the acquisition geometry, the system matrix size can be reduced by a factor corresponding to the number of acquired projections. Such an important decrease in size allows the system matrix to be precomputed, and loaded all at once into memory prior to reconstruction. By carefully ordering the field of view voxels and the sinogram data, reconstruction speed is also enhanced by a cache-oblivious computer implementation. The reconstruction algorithm is also compatible with the ordered-subsets acceleration method. A final polar-to-Cartesian transformation is applied to the reconstructed image in order to allow proper visualization.

The ray-tracing and reconstruction algorithms were implemented in polar representation. Large 3D system matrices were calculated in cylindrical and spherical coordinates, and the performance assessed against Cartesian ray-tracers in terms of speed and memory requirements. Images of analytical phantoms were successfully reconstructed in both cylindrical and spherical coordinates. Fully 3D images of phantoms and small animals were acquired with a Gamma Medica Triumph X-O small animal CT scanner and reconstructed using the manufacturer's software and the proposed polar approach to demonstrate the accuracy and robustness of the later. The noise was found to be reduced while preserving the same level of spatial resolution, without noticeable polar artifacts.

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 more easily performed using general-purpose personal computers.