A practical analysis of scatter-to-primary ratio after beam hardening correction for x-ray CT

Scatter and beam hardening degrade image quality for X-ray computed tomography (CT). Applying beam hardening correction before scatter being fully removed may be needed in some scenarios. In this paper, we theoretically analyze the outcome of beam hardening correction with scatter uncorrected. Using the effective spectrum of CT system, beam hardening correction function and its derivatives can be explicitly derived and used, along with a Taylor expansion, to approximate the change of scatter-to-primary ratio (SPR) after beam hardening correction. Two types of SPR compensations are compared using cone- and fan-beam scans of a CatPhan phantom on a tabletop cone-beam CT system, validating our analysis to be accurate in practical applications.