Fundamental limits for the calculation of scattering corrections within X-ray
computed tomography (CT) are found within the independent atom approximation from an
analysis of the cross sections, CT geometry, and the Nyquist sampling theorem,
suggesting large reductions in computational time compared to existing methods. By
modifying the scatter by less than 1 %, it is possible to treat some of the elastic
scattering in the forward direction as inelastic to achieve a smoother elastic
scattering distribution. We present an analysis showing that the number of samples
required for the smoother distribution can be greatly reduced. We show that fixed
forced detection can be used with many fewer points for inelastic scattering, but
that for pure elastic scattering, a standard Monte Carlo calculation is preferred.
We use smoothing for both elastic and inelastic scattering because the intrinsic
angular resolution is much poorer than can be achieved for projective tomography.
Representative numerical examples are given.