Functional positron emission tomography (fPET) is a neuroimaging method involving continuous infusion of 18-F-fluorodeoxyglucose (FDG) radiotracer during the course of the PET examination. Compared with the conventional bolus administered static FDG PET which provides only a snapshot of the averaged glucose uptake into the brain in a limited dynamic time window, fPET offers a significantly wider time window to study the dynamics of glucose uptake. Several earlier studies have applied fPET to investigate brain FDG uptake and study its relationship with functional magnetic resonance imaging (fMRI). However, due to the unique characteristics of fPET signals, modelling of the fPET signal is a complex task and poses challenges for accurate interpretation of the results. This study applies independent component analysis (ICA) to analyze resting state fPET data, and to compare the performance of ICA and general linear modelling (GLM) for estimation of brain activation in response to tasks. The fPET signal characteristics were compared using GLM and ICA methods to model the fPET visual activation data. Our aim was to evaluate GLM and ICA methods for analyzing task fPET datasets and present ICA method in the analysis of resting state fPET datasets. Using both simulation and in-vivo experimental datasets, we show that both methods can successfully identify task related brain activation. We report fPET metabolic resting state brain networks analyzed using the fPET ICA method in a cohort of healthy subjects. Functional PET provides a unique method to map dynamic changes of glucose uptake in the resting human brain and in response to extrinsic stimulation.