Efficient scatter modelling for incorporation in maximum likelihood reconstruction

Definition of a simplified model of scatter which can be incorporated in maximum 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 scatter estimation is described in which the spatial scatter distribution is implemented as a spatially invariant convolution for points of constant depth in tissue. The scatter estimate is weighted by a space-dependent build-up factor based on the measured attenuation in tissue, Monte Carlo simulation 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) reconstruction algorithm. The scatter estimate was incorporated as a constant term in subsequent iterations rather than modifying the scatter estimate each iteration. Monte Carlo simulation was used to demonstrate that the scatter estimate does not change significantly provided at least two iterations OSEM reconstruction, subset size 8, is used. Complete scatter-corrected reconstruction of 64 projections of 40x128 pixels was achieved in 38 min using a Sun Sparc20 computer.