We describe a method to directly estimate Patlak parameters from list mode data. Based on the Patlak model, the uptake rate function of each voxel can be written as a linear combination of the blood input function and its integral, with the slope and intercept of the Patlak model as the corresponding weight. The positron emission rate in each voxel is then modeled as an inhomogeneous Poisson process with this rate function. The Patlak parameters are estimated directly from list mode data by maximizing the objective function, formed by the sum of the likelihood of arrival times and a spatial smoothness penalty, using a convergent four dimensional incremental gradient algorithm. Fully four dimensional simulations in a liver phantom demonstrate application of this method to realistic time activity curves.