A cautionary note on the use of positivity constrained reconstructions for quantification of regional PET imaging data

Positively constrained maximum likelihood (ML) reconstructions in PET eliminate the negative values associated with unconstrained least squares (LS) - more commonly known as filtered back-projection (FBP). This is desirable for certain qualitative imaging tasks, however, it is not clear if there is a significant benefit for quantitative analysis of dynamic data. We consider a situation where the goal is to quantify the mean uptake in a tissue region of interest using data reconstructed with or without positivity constraints. A theoretical analysis is used to show that averaging unconstrained data is a sufficient statistic for estimation of the regional mean. This calculation casts some doubt over averaging constrained data. We use simulation sto investigate the effect of positivity constraint on mixture model analysis of dynamic data. The results show that the positivity constraint may cause bias in estimation of physiological parameters.