Iterative image reconstruction in helical cone-beam x-ray CT using a stored system matrix approach

We present a stored system matrix (SM) approach for iterative x-ray CT image reconstruction with helical cone-beam geometry. Because of the symmetry of a helical source trajectory, it is sufficient to calculate and store the SM entries for one transaxial slice only and for all source positions illuminating the slice. This is made possible by (1) selecting the reconstruction slice thickness to be an integer multiple of the source translation per projection view, and (2) discretizing the 3D reconstruction volume on a rotated stack of slices. Using the proposed method, the memory requirement for reconstructing a full field-of-view of clinical scanners is manageable on current computing platforms. The same storage principle can be generalized and applied to volume-of-interest (VOI) image reconstruction for helical cone-beam CT. In this case, the stored SM entries correspond to a partial- or full-ring region on one transaxial slice, and for all source positions illuminating the ring. The size and location of the ring depend on the size and the location of the VOI and the scan geometry. We demonstrate by both computer simulations and clinical patient data the speed and efficacy of iterative image reconstruction using the stored SM approach.