A system has been developed to rapidly calculate images of parametric rate constants, without acquiring dynamic frame data for clinical positron emission tomography (PET). This method is based on the weighted-integration algorithms for the two- and three-compartment models, and hardware developments (real-time operation and a large cache memory system) in HEADTOME-IV, which enables the acquisition of multiple sinograms with independent weight integration functions. Following the administration of the radio-tracer, the scan is initiated to collect multiple time-weighted, integrated sinograms with three weight functions. These sinograms are reconstructed and the images, with the arterial blood data, are inserted into the operational equations to provide parametric rate constant images. The implementation of this method has been tested in H215O and 18F-fluorophenylalanine (18FPHE) studies based on a two-compartment model, and in a 18FDG study based on the three-compartment model. A volunteer study, completed for each compound, yielded results consistent with those produced by existing non-linear fitting methods. Thus, this system is capable of rapid generation of quantitative physiological functional images, without dynamic data acquisition, and will be of great advantage for clinical use of PET.