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, in which the number of operations per photon per image slice scales at less than the dimension N of the reconstructed image. The method focuses on the mesh of grid lines which delineate the pixels in the image, rather than on the pixels themselves, and involves computation of the intersection of back-projected Compton cones with just the outermost edges in the image and those grid lines near these image boundary intersection points, for each plane (or slice) of the image. Depending on the orientation of the back projected cone and the image space grid lines, between 4 and N+4 determinations (by quadratic solution) of cone/mesh intersections are required per image slice per photon. Thus the total number of floating point operations per image slice scales as 4 to N+4 times the number of detected photons. Three dimensional back-projections can be obtained simply by stepping through the sequence of planes in the image space parallel to the Compton aperture. Back-projected images are presented, using data generated by Monte Carlo simulations of a practical detector configuration and various source distributions.