Kinetic analysis is an essential tool of Positron Emission Tomography image analysis. However it requires a pure tissue time activity curve (TAC) in order to calculate the system parameters. Pure tissue TACs are particularly difficult to obtain in the brain as the low resolution of PET means almost all voxels are a mixture of tissues. Factor analysis explicitly accounts for mixing but is an underdetermined problem that can give arbitrary results. A joint factor and kinetic analysis is proposed whereby factor analysis explicitly accounts for mixing of tissues. Hence, more meaningful parameters are obtained by the kinetic models, which also ensure a less ambiguous solution to the factor analysis. The method was tested using a cylindrical phantom and the 18F-DOPA data of a brain cancer patient.