A FAST PROJECTOR-BACKPROJECTOR PAIR MODELING THE ASYMMETRIC, SPATIALLY VARYING SCATTER RESPONSE FUNCTION FOR SCATTER COMPENSATION IN SPECT IMAGING

We have previously developed a method, slab derived scatter estimation (SDSE), for quickly and accurately modeling the asymmetric, spatially varying scatter response function in uniformly attenuating objects wi th convex surfaces. This model has been implemented in a projector-bac kprojector that, when combined with iterative reconstruction technique s, provides accurate scatter compensation in single-photon emission co mputed tomography (SPECT). These iterative reconstruction based scatte r compensation techniques have the advantage that they use all detecte d photons, avoiding the noise amplification occurring with subtraction based schemes. In addition, scatter compensation with iterative recon struction does not involve the use of arbitrary adjustable parameters. In this paper we present a new fast algorithm for implementing SDSE t hat reduces computation time by a factor of 16 compared to a direct im plementation. Projection data computed with the new algorithm compare well with that from Monte Carlo simulations. When combined with faster computers and iterative reconstruction algorithms that converge rapid ly, this fast projector-backprojector pair makes iterative reconstruct ion based scatter compensation feasible.