Efficient forward projection through discrete data sets using tri-linear interpolation

Forward projection through discrete data sets is a major step in all iterative reconstruction methods. Based on the assumption that the true object function can be described adequately by tri-linear interpolation between the samples, which are located on a cubic grid, the authors propose an efficient and accurate method to calculate line integrals: the line is divided into segments separated by the surfaces of the grid and within each segment the integration is done using Simpson's rule.