Variability Assessment in Positron Emission Tomography and Related Generalized Deconvolution Models

The problem of variance assessment for positron emission tomography (PET) image reconstructions is considered in the context of generalized deconvolution. A refinement of an approximate technique proposed by Carson and colleagues is examined. Computational implications of representing the reconstruction kernel in terms of a weighted sum of Gaussian densities are developed. Bias and variance characteristics of the resulting variance estimators are examined by numerical simulation. For typical regions, the error in estimated standard deviations is found to be on the order of 10%. The use of smoothing to obtain more reliable pointwise variance estimators is described, and some theoretical analysis of this technique is carried out. For the PET application, simulations suggest that the percent improvement in the root mean squared error accuracy of pointwise variance estimators obtained by smoothing can be on the order of 30%. A practical application of the methodology to a PET study is presented.