Unmixing is a ubiquitous task in hyperspectral image analysis which consists in jointly extracting typical spectral signatures and estimating their respective proportions in the voxels, providing an explicit spatial mapping of these elementary signatures over the observed scene. Inspired by this approach, this paper aims at proposing a new framework for analyzing dynamic positron emission tomography (PET) images. More precisely, a PET-dedicated mixing model and an associated unmixing algorithm are derived to jointly estimate time-activity curves (TAC) characterizing each type of tissues, and the proportions of those tissues in the voxels of the imaged brain. In particular, the TAC corresponding to the specific binding class is expected to be voxel-wise dependent. The proposed approach allows this intrinsic spatial variability to be properly modeled, mitigated and quantified. Finally, the main contributions of the paper are twofold: first, we demonstrate that the unmixing concept is an appropriate analysis tool for dynamic PET images; and second, we propose a novel unmixing algorithm allowing for variability, which significantly improves the analysis and interpretation of dynamic PET images when compared with state-of-the-art unmixing algorithms.