Acceleration of a model based scatter correction scheme for SPECT by use of an unmatched projector-backprojector

In this paper three scatter compensation schemes are considered. The three schemes are all based on a previously developed scatter model. Reconstruction is achieved using the iterative Expectation-Maximization Maximum-Likelihood algorithm. The schemes consist of: (a) including the model in both the forward and backprojector, (b) just including the model in the forward projector, and (c) implementing the model in a subtraction scheme. Monte-Carlo simulated projection data are used to test the accuracy, convergence properties, and noise properties of the three scatter compensation schemes. The results show that all three correction schemes yield images which are similar in terms of accuracy to that obtained from constructing 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 does not, in general, perform significantly better than the subtraction scheme, but requires longer For reconstruction. The correction scheme in which the scatter model is included in both the forward and backprojectors is shown to produce accurate images with signal to noise ratios higher than even a perfect scatter rejection scheme. While the scatter correction scheme with the model in both forward and backprojectors has superior noise properties to the other algorithms, the results suggest that the subtraction scheme, with its faster convergence properties, will probably prove most useful for routine clinical scatter compensation