Fast algorithm for list mode back-projection of Compton scatter camera data

A fast algorithm is presented for back-projection of Compton camera projection data in a list mode fashion for which the number of operations per photon per image slice scales at less than the dimension of the image space. The method focuses on the mesh of grid lines which delineate pixel (or voxel) boundaries, rather than on the pixels themselves, and involves computation of the intersection of back-projected Compton cones with just the image space boundaries and those grid lines near the boundary intersection points for each plane of the image space. Depending on the orientation of the back projected cone and the image grid lines, between 4 and N+4 determinations (by quadratic solution) of cone/mesh intersections are required per image slice per photon, where N is the dimension of the image space. Thus the total number of floating point operations for this method from 4 to N+4 times the number of operations in solving a quadratic for each photon. Back-projections for tomographic reconstructions can be readily obtained by stepping through the sequence of planes n the image space parallel to the Compton aperture. Back-projected images are presented, using data generated by Monte Carlo simulation of a practical detector configuration and various source distributions