Dynamic positron emission tomography (PET) imaging technique enables the measurement of neuroreceptor distributions corresponding to anatomic structures, and thus, allows image-wide quantification of physiological and biochemical parameters. Accurate quantification of the concentration of neuroreceptor has been the objective of many research efforts. Compartment modeling is the most widely used approach for receptor binding studies. However, current compartment-model-based methods often either require intrusive collection of accurate arterial blood measurements as the input function, or assume the existence of a reference region. To obviate the need for the input function or a reference region, in this paper, we propose to estimate the input function. We propose a novel concept of activity subspace, and estimate the input function by the analysis of the intersection of the activity subspaces. Then, the input function and the distribution volume (DV) parameter are refined and estimated iteratively. Thus, the underlying parametric image of the total DV is obtained. The proposed method is compared with a blind estimation method, iterative quadratic maximum-likelihood (IQML) via simulation, and the proposed method outperforms IQML. The proposed method is also evaluated in a brain PET dataset.