A dynamic sequence of positron emission tomography (PET) images gives rise to the possibility of creating images of in vivo tissue metabolism. For this reason PET is potentially a valuable instrument in the study of human biology and medicine. The analysis of dynamic PET data to produce metabolic images is a challenging problem from a statistical point of view. For example, a typical data set arising in the study of cerebral glucose utilization has on the order of 30 time-binned images per cross-sectional slice of tissue under examination, each of dimension 128 x 128 pixels. Metabolic imaging requires that the time series at each pixel, known as the time activity curve (TAC), be analysed to produce an estimate of local metabolism. This paper describes a mixture analysis approach to the construction of such metabolic images. In the approach the TAC at a given pixel is expressed as a weighted sum of sub-TACs corresponding to homogeneous tissues represented at the pixel. Estimates of tissue metabolism at the pixel are then constructed as a weighted sum of the metabolism associated with the individual sub-TACs. The procedure is illustrated by application to a [F-18]-labelled deoxyglucose study in a patient with a brain tumour. The ability to map simultaneously a range of parameters related to the transport and biochemical transformation of the radio-tracer, demonstrates the potential power of dynamic PET.