An analysis of scatter characteristics in x-ray CT spectral correction

X-ray scatter remains a major physics challenge in volumetric computed tomography (CT), whose physical and statistical behaviors have been commonly leveraged in order to eliminate its impact on CT image quality. In this work, we conduct an in-depth derivation of how the scatter distribution and scatter to primary ratio (SPR) will change during the spectral correction, leading to an interesting finding on the property of scatter. Such a characterization of scatter's behavior provides an analytic approach of compensating for the SPR as well as approximating the change of scatter distribution after spectral correction, even though both of them might be significantly distorted as the linearization mapping function in spectral correction could vary a lot from one detector pixel to another. We conduct an evaluation of SPR compensations (SPRCs) on a Catphan phantom and an anthropomorphic chest phantom to validate the characteristics of scatter. In addition, this scatter property is also directly adopted into CT imaging using a spectral modulator with flying focal spot technology (SMFFS) as an example to demonstrate its potential in practical applications. For cone-beam CT (CBCT) scans at both 80 and 120 kVp, CT images with accurate CT numbers can be achieved after spectral correction followed by the appropriate SPRC based on our presented scatter property. In the case of the SMFFS based CBCT scan of the Catphan phantom at 120 kVp, after a scatter correction using an analytic algorithm derived from the scatter property, CT image quality was significantly improved, with the averaged root mean square error reduced from 297.9 to 6.5 Hounsfield units.