We propose a novel method to directly estimate parametric images from listmode PET data for reversible tracers based on an inhomogeneous Poisson process model. We use a relative equilibrium graphical model, similar to the Logan plot, to linearize the problem. A static sinogram from time of tracer injection to the steady state is incorporated to improve the ill-conditioning of the estimation problem. Cramer-Rao analysis and Monte-Carlo simulation demonstrate that our method improves the conditioning of the estimation problem and provides higher contrast recovery and smaller standard deviation compared with a sinogram based direct estimation approach.