A projector/backprojector with slice-to-slice blurring for efficient three-dimensional 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 three-dimensional (3-D) first-order scatter in SPECT, also using an efficient slice-to-slice blurring technique. The scatter response is estimated from a known nonuniform attenuation distribution map. It is assumed that the probability of detection of a first-order scattered photon from a photon that is emitted in a given source voxel and scattered in a given scatter voxel is proportional to the attenuation coefficient value at that voxel. Monte Carlo simulations of point sources and an MCAT torso phantom were used to verify the accuracy of the proposed projector/backprojector model. An experimental Jaszczak torso/cardiac phantom SPECT study was also performed. For a 64×64×64 image volume, it took 8.7 s to perform each iteration per slice on a Sun ULTRA Enterprise 3000 (167 MHz, 1 Gbyte RAM) computer, when modeling 3-D scatter, attenuation, and system geometric response functions. The main advantage of the proposed method is its easy implementation and the possibility of performing reconstruction in clinically acceptable time.