A Look-Up Table-Based Ray Integration Framework for 2-D/3-D Forward and Back Projection in X-Ray CT

Iterative algorithms have become increasingly popular in computed tomography (CT) image reconstruction, since they better deal with the adverse image artifacts arising from low radiation dose image acquisition. But iterative methods remain computationally expensive. The main cost emerges in the projection and back projection operations, where accurate CT system modeling can greatly improve the quality of the reconstructed image. We present a framework that improves upon one particular aspect - the accurate projection of the image basis functions. It differs from current methods in that it substitutes the high computational complexity associated with accurate voxel projection by a small number of memory operations. Coefficients are computed in advance and stored in look-up tables parameterized by the CT system's projection geometry. The look-up tables only require a few kilobytes of storage and can be efficiently accelerated on the GPU. We demonstrate our framework with both numerical and clinical experiments and compare its performance with the current state-of-the-art scheme - the separable footprint method.