Implementation of a model-based nonuniform scatter correction scheme for SPECT

In this paper four scatter-compensation schemes are considered. The four schemes are all based on a previously developed two-dimensional (2-D) scatter model. Reconstruction is achieved using the iterative expectation-maximization maximum-likelihood (EM-ML) algorithm. The schemes consist of: 1) including the model in both the forward and back projector; 2) just including the model in the forward projector; 3) and 4) implementing the model in a subtraction and addition scheme, respectively. Monte Carlo simulated projection data are used to test the accuracy, convergence properties, and noise properties of the four scatter-compensation schemes. Data are simulated for both uniformly and nonuniformly attenuating objects. The results show that all four correction schemes yield images which are similar in terms of accuracy to that obtained from reconstructing scatter-free data. The subtraction scheme is shown to converge faster than the other compensation schemes, both in terms of iterations and actual time required for reconstruction. The scheme in which the model is only used in the forward-projector and the scatter-addition scheme both performs slightly better, in terms of signal-to-noise ratio (SNR), than the subtraction scheme. However, the forward projector scheme requires significantly more CPU time for reconstruction. The correction scheme in which the scatter model was included in both the forward and backprojectors is shown to produce accurate images with SNR's higher than even a perfect scatter rejection scheme. While the scatter correction scheme with the model in both the forward projector and backprojector has superior noise properties to the other algorithms, the results suggest that the faster subtraction/addition schemes will probably prove most useful for routine clinical scatter compensation.