Efficient scatter modelling for incorporation in maximum likelihood reconstruction

Definition of a simplified model of scatter which can be incorporated in ma ximum likelihood reconstruction for single-photon emission tomography (SPET ) continues to be appealing; however, implementation must be efficient for it to be clinically applicable. In this paper an efficient algorithm for sc atter estimation is described in which the spatial scatter distribution is implemented as a spatially invariant convolution for points of constant dep th in tissue. The scatter estimate is weighted by a space-dependent build-u p factor based on the measured attenuation in tissue, Monte Carlo simulatio n of a realistic thorax phantom was used to validate this approach. Further efficiency was introduced by estimating scatter once after a small number of iterations using the ordered subsets expectation maximisation (OSEM) rec onstruction algorithm. The scatter estimate was incorporated as a constant term in subsequent iterations rather than modifying the scatter estimate ea ch iteration. Monte Carlo simulation was used to demonstrate that the scatt er estimate does not change significantly provided at least two iterations OSEM reconstruction, subset size 8, is used. Complete scatter-corrected rec onstruction of 64 projections of 40x128 pixels was achieved in 38 min using a Sun Sparc20 computer.