An analytical approach to estimating the first order x-ray scatter in heterogeneous medium.

X-ray scatter estimation in heterogeneous medium is a challenge in improving the quality of diagnostic projection images and volumetric image reconstruction. For Compton scatter, the statistical behavior of the first order scatter can be accurately described by using the Klein-Nishina expression for Compton scattering cross section provided that the exact information of the medium including the geometry and the attenuation, which in fact is unknown, is known. The authors present an approach to approximately separate the unknowns from the Klein-Nishina formula and express the unknown part by the primary x-ray intensity at the detector. The approximation is fitted to the exact solution of the Klein-Nishina formulas by introducing one parameter, whose value is shown to be not sensitive to the linear attenuation coefficient and thickness of the scatterer. The performance of the approach is evaluated by comparing the result with those from the Klein-Nishina formula and Monte Carlo simulations. The approximation is close to the exact solution and the Monte Carlo simulation result for parallel and cone beam imaging systems with various field sizes, air gaps, and mono- and polyenergy of primary photons and for nonhomogeneous scatterer with various geometries of slabs and cylinders. For a wide range of x-ray energy including those often used in kilo- and megavoltage cone beam computed tomographies, the first order scatter fluence at the detector is mainly from Compton scatter. Thus, the approximate relation between the first order scatter and primary fluences at the detector is useful for scatter estimation in physical phantom projections.