Analytical Calculation of the Compton Single Scatter Component of Pencil Beam Scatter Kernel for Scatter Correction in kV Cone Beam CT (kV-CBCT)

The accuracy of conventional superposition or convolution methods for scatter correction in kV-CBCT is usually compromised by the spatial variation of pencil-beam scatter kernel (PBSK) due to finite size, irregular external contour and heterogeneity of the imaged object. This study aims to propose an analytical method to quantify the Compton single scatter (CSS) component of the PBSK, which dominates the spatial distribution of total scatter assuming that multiple scatter can be estimated as a constant background and Rayleigh scatter is the secondary source of scatter. The CSS component of PBSK is the line integration of scatter production by incident primary photons along the beam line followed by the post-scattering attenuation as the scattered photons traverse the object. We propose to separate the object-specific attenuation term from the line integration and equivalently replace it with an average value such that the line integration of scatter production is object independent but only beam specific. We derived a quartic function formula as an approximate solution to the spatial distribution of the unattenuated CSS component of PBSK. The “effective scattering center” is introduced to calculate the average attenuation. The proposed analytical framework to calculate the CSS was evaluated using parameter settings of the On-Board Imager kV-CBCT system and was found to be in high agreement with the reference results. The proposed method shows highly increased computational efficiency compared to conventional analytical calculation methods based on point scattering model. It is also potentially useful for correcting the spatial variant PBSK in adaptive superposition method.