A projector/backprojector with slice-to-slice blurring for efficient three-dimensional scatter modeling

Scatter correction is an important factor in single photon emission compute d tomography (SPECT), Many scatter correction techniques, such as multiple- window subtraction and intrinsic modeling with iterative algorithms, have b een under study for many years. Previously, we developed an efficient slice -to-slice blurring technique to model attenuation and system geometric resp onse in a projector/backprojector pair, which was used in an ML-EM algorith m 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 as sumed that the probability of detection of a first-order scattered photon f rom a photon that is emitted in a given source voxel and scattered in a giv en scatter voxel is proportional to the attenuation coefficient value at th at voxel, Monte Carlo simulations of point sources and an MCAT torso phanto m were used to verify the accuracy of the proposed projector/backprojector model. An experimental Jaszczak torso/cardiac phantom SPECT study tvas also performed, For a 64 x 64 x 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) c omputer, when modeling 3-D scatter, attenuation, and system geometric respo nse functions. The main advantage of the proposed method is its easy implem entation and the possibility of performing reconstruction in clinically acc eptable time.