  To analyze dynamic positron emission tomography (PET) images, various generic
multivariate data analysis techniques have been considered in the literature,
such as principal component analysis (PCA), independent component analysis
(ICA), factor analysis and nonnegative matrix factorization (NMF).
Nevertheless, these conventional approaches neglect any possible nonlinear
variations in the time activity curves describing the kinetic behavior of
tissues with specific binding, which limits their ability to recover a
reliable, understandable and interpretable description of the data. This paper
proposes an alternative analysis paradigm that accounts for spatial
fluctuations in the exchange rate of the tracer between a free compartment and
a specifically bound ligand compartment. The method relies on the concept of
linear unmixing, usually applied on the hyperspectral domain, which combines
NMF with a sum-to-one constraint that ensures an exhaustive description of the
mixtures. The spatial variability of the signature corresponding to the
specific binding tissue is explicitly modeled through a perturbed component.
The performance of the method is assessed on both synthetic and real data and
is shown to compete favorably when compared to other conventional analysis
methods. The proposed method improved both factor estimation and proportions
extraction for specific binding. Modeling the variability of the specific
binding factor has a strong potential impact for dynamic PET image analysis.
