Our recent research is concerned with the development of techniques for the> estimation of parametric data from dynamic positron emission tomographic> (PET) brain images. Improved sensitivity in quantification of the metabolic processes in the brain will be useful for medical studies of disease progression and drug impacts in patients with Alzheimer's Disease. While PET is a useful diagnostic tool due to its ability to image biological functions in vivo, unlike other imaging modalities, dynamic PET data suffers from low count statistics, leading to poor signal-to-noise ratios. This complicates the solution of the inverse problem for estimation of kinetic parameters which in our work describe the dynamics of the tracer, fluoro-deoxy-glucose (FDG). Our analysis brings together several numerical techniques, from thecompartmental model describing the biological function, to the inverse problem which this generates for the parameter estimation, to techniques for image restoration of very poor data, combined with both a robust statistical validation of the entire process and practical and efficient design of the underlying method. In this presentation I review some of the challenges associated with generation of global parametric image, and then focus on recent work for simultaneous estimation of the input to the compartmental model.