Approximation of voxel-level variances from spatial-variances for single scan PET data

Variance is one of the important metrics which is very useful in characterizing PET images, in particular when used in parameter estimation of dynamic PET data and in comparing different reconstruction algorithms or correction methods. Due to the nonlinear nature of some iterative reconstruction algorithms, (e.g., the ordered subset expectation maximization (OSEM)), voxel-level variance estimation can be challenging. However, although such estimation can be achieved via techniques such as Monte Carlo and the bootstrap, these techniques require a lot of computational time and are often impractical. In this work it was investigated whether the voxel-level variance/standard deviation can be estimated based on a single PET scan for any given region of interest (ROI) as long as the region is homogeneous and of large enough size to offer acceptable accuracy. Such variance estimation was here applied to two brain phantom scans with varying count level and a single human brain scan of [¹¹C]raclopride by considering a homogeneous neighbourhood of a given size for any individual voxel. The results were then compared to the variance estimation based on the bootstrap method applied to the same PET scans. It is shown that the single scan method can approximate the voxel-level standard deviation (SD) with a reasonable accuracy (15 %) for noisy and low count datasets but it breaks down for higher count levels. For large and homogeneous regions larger voxel neighbourhoods achieve better agreement with the bootstrap estimation of SD. However, in the striatum the size of the voxel neighbourhood has to be smaller due to the size of the region, otherwise the homogeneity condition will not be met. The advantage of this approximate method is that it is very simple to apply without any extra theoretical assumptions.