  Positron Emission Tomography (PET) is an imaging technique which can be used
to investigate chemical changes in human biological processes such as cancer
development or neurochemical reactions. Most dynamic PET scans are currently
analyzed based on the assumption that linear first order kinetics can be used
to adequately describe the system under observation. However, there has
recently been strong evidence that this is not the case. In order to provide an
analysis of PET data which is free from this compartmental assumption, we
propose a nonparametric deconvolution and analysis model for dynamic PET data
based on functional principal component analysis. This yields flexibility in
the possible deconvolved functions while still performing well when a linear
compartmental model setup is the true data generating mechanism. As the
deconvolution needs to be performed on only a relative small number of basis
functions rather than voxel by voxel in the entire 3-D volume, the methodology
is both robust to typical brain imaging noise levels while also being
computationally efficient. The new methodology is investigated through
simulations in both 1-D functions and 2-D images and also applied to a
neuroimaging study whose goal is the quantification of opioid receptor
concentration in the brain.
