System matrix computation vs storage on GPU: A comparative study in cone beam CT

Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersection distances between the trajectories of photons and the object, also called ray tracing or system matrix computation. This work focused on the thin-ray model is aimed at comparing different system matrix handling strategies using graphical processing units (GPUs).

In this work, the system matrix is modeled by thin rays intersecting a regular grid of box-shaped voxels, known to be an accurate representation of the forward projection operator in CT. However, an uncompressed system matrix exceeds the random access memory (RAM) capacities of typical computers by one order of magnitude or more. Considering the RAM limitations of GPU hardware, several system matrix handling methods were compared: full storage of a compressed system matrix, on-the-fly computation of its coefficients, and partial storage of the system matrix with partial on-the-fly computation. These methods were tested on geometries mimicking a cone beam CT (CBCT) acquisition of a human head. Execution times of three routines of interest were compared: forward projection, backprojection, and ordered-subsets convex (OSC) iteration.

A fully stored system matrix yielded the shortest backprojection and OSC iteration times, with a 1.52× acceleration for OSC when compared to the on-the-fly approach. Nevertheless, the maximum problem size was bound by the available GPU RAM and geometrical symmetries. On-the-fly coefficient computation did not require symmetries and was shown to be the fastest for forward projection. It also offered reasonable execution times of about 176.4 ms per view per OSC iteration for a detector of 512 × 448 pixels and a volume of 384³ voxels, using commodity GPU hardware. Partial system matrix storage has shown a performance similar to the on-the-fly approach, while still relying on symmetries.

Partial system matrix storage was shown to yield the lowest relative performance. On-the-fly ray tracing was shown to be the most flexible method, yielding reasonable execution times. A fully stored system matrix allowed for the lowest backprojection and OSC iteration times and may be of interest for certain performance-oriented applications.