UBES: Unified scatter correction using ultrafast Boltzmann equation solver for conebeam CT

Abstract

A semi-analytical solution to the unified Boltzmann equation is constructed to exactly describe the scatter distribution on a flat-panel detector for high-quality conebeam CT (CBCT) imaging. The solver consists of three parts, including the phase space distribution estimator, the effective source constructor and the detector signal extractor. Instead of the tedious Monte Carlo solution, the derived Boltzmann equation solver achieves ultrafast computational capability for scatter signal estimation by combining direct analytical derivation and time-efficient one-dimensional numerical integration over the trajectory along each momentum of the photon phase space distribution. The execution of scatter estimation using the proposed ultrafast Boltzmann equation solver (UBES) for a single projection is finalized in around 0.4 seconds. We compare the performance of the proposed method with the state-of-the-art schemes, including a time-expensive Monte Carlo (MC) method and a conventional kernel-based algorithm using the same dataset, which is acquired from the CBCT scans of a head phantom and an abdominal patient. The evaluation results demonstrate that the proposed UBES method achieves comparable correction accuracy compared with the MC method, while exhibits significant improvements in image quality over learning and kernel-based methods. With the advantages of MC equivalent quality and superfast computational efficiency, the UBES method has the potential to become a standard solution to scatter correction in high-quality CBCT reconstruction.

Keywords: Boltzmann equation; Conebeam CT; Image reconstruction; Scatter correction.