Kinetic modeling of dynamic PET data requires knowledge of tracer concentration in blood plasma, described by the arterial input function (AIF). Arterial blood sampling is the gold standard for AIF measurement, but is invasive and labour intensive. A number of methods have been proposed to accurately estimate the AIF directly from blood sampling and/or imaging data. Here we consider fitting a patient-adaptive mixture of historical population time course profiles to estimate individual AIFs. Travel time of a tracer atom from the injection site to the right ventricle of the heart is modeled as a realization from a Gamma distribution, and the time this atom spends in circulation before being sampled is represented by a subject-specific linear mixture of population profiles. These functions are estimated from independent population data. Individual AIFs are obtained by projection onto this basis of population profile components. The model incorporates knowledge of injection duration into the fit, allowing for varying injection protocols. Analyses of arterial sampling data from 18F-FDG, 15O-H2O and 18F-FLT clinical studies show that the proposed model can outperform reference techniques. The statistically significant gain achieved by using population data to train the basis components, instead of fitting these from the single individual sampling data, is measured on the FDG cohort. Kinetic analyses of simulated data demonstrate the reliability and potential benefit of this approach in estimating physiological parameters. These results are further supported by numerical simulations that demonstrate convergence and stability of the proposed technique under varying training population sizes and noise levels.