There are five main steps which are common to the simulation based scatter correction methods, including analytical and Monte Carlo approaches. These are:
1. Reconstruct the attenuation volume: This is normally done using conventional 2D reconstruction of the blank and transmission data. However, any method that produces an accurate map of linear attenuation coefficients in units cm-1) in the body can be used, including appropriately registered and scaled CT data if available.
2. Reconstruct an initial estimate of the emission volume: Different approaches have been adopted for this step. Watson et al use 3D reconstruction of the measured projections which include scatter , while Ollinger determines the initial emission estimate iteratively from direct plane data only . He showed that the process converges rapidly and requires only a small number of iterations. In the Monte Carlo implementation due to Holdsworth et al , the initial estimate is obtained by performing the analytical scatter simulation technique (57), a as implemented on the EXACT HR+ scanner (CTI PET Systems, Knoxville,TN).
3. Estimate the scatter contribution to projections: This is the main step which involves estimating the scatter contributing to direct and oblique emission sinograms as described above for the various simulation techniques. Each of the implementations described includes some means of estimating the scatter contribution due to activity outside the field of view.
4. Scale the scatter estimate: Here the scatter distribution is scaled globally to ensure a good fit between the estimated scatter and the measured projections in regions not sampled by the object (i.e., regions where only scatter is present). Alternatively, if the detection system is modelled accurately including detector efficiencies and energy response, it may be possible to compute a scatter distribution which is intrinsically scaled relative to the measured projections as in a more recent implementation by Watson . In the Monte Carlo approach, the total coincidences in each projection can be simulated as well as the scatter coincidences. Thus, the scaling step simply involves determining the scale factor that yields the same total coincidences in both the estimated and measured projections. This global scale factor is less prone to noise in low count studies than the factor calculated using the scatter tails.
5. Correct 3D emission projections for scatter: The final step is to subtract the estimated scatter from direct and oblique sinograms. In some cases, the scatter estimate is smoothed before subtraction without loss of accuracy since the scatter distribution contains only low spatial frequency components.
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