Pre-processing variance reducing techniques in multispectral positron emission tomography.

Stochastic fluctuations and systematic errors severely restrict the potential of multispectral acquisition to improve scatter correction by energy-dependent processing in high-resolution positron emission tomography (PET). To overcome this limitation, three pre-processing approaches which reduce stochastic fluctuations and systematic errors without degrading spatial resolution were investigated: statistical variance was reduced by smoothing acquired data in energy space, systematic errors due to nonuniform detector efficiency were minimized by normalizing the data in the spatial domain and the overall variance was further reduced by selecting an optimal pre-processing sequence. Selection of the best protocol to reduce stochastic fluctuations entailed comparisons between four smoothing algorithms (prior constrained (PC) smoothing, weighted smoothing (WS), ideal low-pass filtering (ILF) and mean median (MM) smoothing) and permutations of three pre-processing procedures (smoothing, normalization and subtraction of random events). Results demonstrated that spectral smoothing by WS, ILF and MM efficiently reduces the statistical variance in both the energy and spatial domains without observable spatial resolution loss. The ILF algorithm was found to be the most convenient in terms of simplicity and efficiency. Regardless of the position of subtraction of randoms in the sequence, reduction of the systematic errors by normalization followed by spectral smoothing to suppress statistical noise produced the best results. However, subtraction of random events first in the sequence reduces computation load by half since the need to pre-process this distribution before subtraction is removed. In summary, normalizing data in the spatial domain and smoothing data in energy space are essential steps required to reduce systematic errors and statistical variance independently without degrading spatial resolution of multispectral PET data.