To analyze dynamic positron emission tomography (PET) images, various generic multivariate data analysis techniques have been considered in the literature, such as clustering, principal component analysis (PCA), independent component analysis (ICA) and non-negative matrix factorization (NMF). Nevertheless, these conventional approaches generally fail to recover a reliable, understandable and interpretable description of the data. In this paper, we propose an alternative analysis paradigm based on the concept of linear unmixing as an efficient and meaningful way to analyze dynamic PET images. The time-activity curves (TACs) measured in the voxels are modeled as linear combinations of elementary component signatures weighted by their respective concentrations in each voxel. Additionally to the non-negativity constraint of NMF, the proposed unmixing approach ensures an exhaustive description of the mixtures by a sum-to-one constraint of the mixing coefficients. Besides, it allows both the noise and partial volume effects to be handled. Moreover, the proposed method accounts for any possible fluctuations in the exchange rate of the tracer between the free compartment and a specifically bound ligand compartment. Indeed, it explicitly models the spatial variability of the corresponding signature through a perturbed specific binding component. The performance of the method is assessed on both synthetic and real data and compared to other conventional analysis methods.