## Properties of MLEM Reconstruction

The EM algorithm results in an iterative process for estimation consistent with the general iterative flow-chart given in Figure 1. In this case the update is multiplicative, not unlike SMART, with the update simply being the ratio of measured over estimated projections. As the number of iterations increases the likelihood increases, providing an estimate that theoretically is more likely to be close to the true object distribution. In practice, however, the image reaches an optimal visual quality at typically around 16 iterations and, in the absence of any noise constraint, appears progressively more noisy at higher number of iterations (Figure 2). The noise characteristics are appealing, with the variance remaining proportional to number of counts rather than being approximately position-independent as in FBP.9'20 This tends to favour lesion detection in low count areas where the signal to noise ratio can be markedly improved. The ML solution after a large number of iterations is not the most 'desirable' solution as it reflects the actual noisy distribution of emitted counts rather than the underlying activity, whose distribution is likely to be much less variable. In clinical practice it is common to stop at a small number of iterations in order to limit noise. However it should be recognised that the reconstruction does not converge at the same rate for all points. Halting the reconstruction early runs a risk of reducing reconstruction accuracy, which can be avoided by using a larger number of iterations with post-reconstruction smoothing.21 Alternative approaches to controlling noise are discussed in section 6.

There are several attractive theoretical properties of ML-EM although in practice these rarely offer real advantage due to approximations in the system model and the relatively high level of noise in most emission tomography studies. The use of a multiplicative update guarantees positive values and also means that areas outside the object, where zero counts are expected,

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