Quantification of receptor binding studies obtained with PET is complicated by tissue heterogeneity in the sampling image elements pixels and voxels. This effect is caused by a limited spatial resolution of the PET scanner. On the other hand, spatial heterogeneity is often essential in understanding the underlying receptor binding process. In this paper, we propose a likelihood-based framework in the pixel domain for quantitative imaging with or without the input function. Radioligand kinetic parameters are estimated together with the input function. The parameters are initialized by a subspace-based algorithm, and further refined by an iterative likelihood-based estimation procedure. The performances of the proposed scheme is examined by simulations. Real brain PET data are also examined to show the performance in determining the time activity curves and the underlying factor images.