A projector/backprojector with slice-to-slice blurring for efficient 3D scatter modeling

Scatter correction is an important factor in single photon emission computed tomography (SPECT). Many scatter correction techniques, such as multiple-window subtraction and intrinsic modeling with iterative algorithms, have been under study for many years. Previously, the authors developed an efficient slice-to-slice blurring technique to model attenuation and system geometric response in a projector/backprojector pair, which was used in an ML-EM algorithm to reconstruct SPECT data. This paper proposes a projector/backprojector that models the 3D first-order scatter in SPECT, also using an efficient slice-to-slice blurring technique. The scatter response is estimated from a known, non-uniform, attenuation distribution map. It is assumed that the probability of a scatter event at a pixel is proportional to the attenuation coefficient value at that pixel. Monte Carlo simulations of point-sources and a MCAT torso phantom were used to verify the accuracy of the proposed projector/backprojector model. For a 64×64×64 image volume, it took 8.7 seconds to perform each iteration per slice, when modeling 3D scatter, attenuation, and system point response functions. The main advantage of the proposed method is its ease to implement and efficiency in computer calculation