Fast scatter estimation for cone-beam X-ray CT by combined Monte Carlo tracking and Richardson-Lucy fitting

The long computation times that are required to obtain low-noise scatter estimates from Monte Carlo (MC) simulation prohibits the use of such simulations for applications like corrective tomographic reconstruction. In our previous work we have proposed to de-noise scatter estimates obtained from a rapid MC (low number of simulated photons) by employing Richardson-Lucy (RL) fit performed separately on each projection. In this way scatter simulation can be accelerated by up to two orders of magnitude. Here we show an improved algorithm that executes the fit also in the angular direction, thus exploiting a priori knowledge about the smoothness of scatter distributions as a function of projection angle. We validate the speed-up and accuracy achieved with this approach by simulation of digital phantom for a small animal cone-beam X-ray CT system. Results indicate that an acceleration of three-four orders of magnitude over standard MC simulation is achieved. As a result, tracking of 10 ⁴-10⁵ photons/projection is sufficient to arrive at scatter estimates with the same accuracy as obtained using 10 ⁷-10⁹ photons with MC supported only by the established Forced Detection (FD) method. The RL fitting is accurate even for outermost projections in the dataset and for truncated scatter distributions. Such a rapid, robust and accurate scatter simulation makes feasible model based and anatomy dependent scatter correction in X-ray CT and allows for fast simulations of animal and patient studies.