Estimation of the local statistical noise in positron emission tomography revisited: practical implementation

The purpose of this report is to implement novel modifications to overcome the limitations of an existing algorithm for estimating the local statistical noise in a positron emission tomography (PET) image without performing repeated measures. The original algorithm is based on a modification of the filtered back-projection algorithm that allows the variance to be estimated using only a single sinogram. In addition, the effects of photon absorption, random coincidences, radioactive decay, and detector nonuniformity are taken into account. However, there are some limitations when applying this method with modern scanners. In particular, it is common practice to interleave the projections in the sinogram (to increase the sampling rate along each projection) and to perform an interpolation when actually back-projecting to reconstruct the images. Both of these procedures introduce covariance among the elements of the projections, which is cumbersome and impractical to deal with using the existing technique for creating a variance image. An alternative image reconstruction scheme that is shown to be equivalent to image reconstruction using traditional filtered back-projection greatly simplifies the estimation of the variance image. The proposed methods were tested by Monte Carlo simulations and by using repeated scans of a uniform phantom filled with F-18. Results demonstrate that the proposed methods are very rigorous and stable when compared to calculations of the local variance using either repeated measures with a large number of measurements, or region-of-interest estimates of the variance, assuming homogeneous variance structure. In addition, strategies for extending the proposed technique are discussed that would permit the estimation of the variance due to measurement error of a pixel in a brain map from both single subjects and pooled group data.