Title: Unmixing Dynamic PET images
Abstract: Positron emission tomography formation has been addressed as a linear combination of time-activity curves (TACs) by several approaches, such as clustering, blind-source separation (BSS) and non-negative matrix factorization (NMF). Nevertheless, the high correlation between TACs along with the great level of noise of this type of images brings forth an extremely non-convex problem not easily solvable by the already proposed methods.
In this context, hyperspectral unmixing, a widely known concept in remote sensing, appears as an answer to reduce the number of possible solutions to this problem. It is formulated as a Linear Mixing Model(LMM) where the ensemble of signatures or sources are called endmembers and the matrices containing the proportions of those endmembers per voxel are called abundances. Additionally to the non-negativity constraint of NMF, unmixing settles a sum-to-one constraint to the abundances. Furthermore, recent works have proposed unmixing acknowledging endmember variability. In PET context, these variabilities could account for the fluctuations in the exchange rate of tracer between the free compartment and a specifically bound ligand compartment.
In this work, we propose an unmixing approach based on a perturbed specific binding endmember (PSBE) into a linear mixing model (LMM). The performance of our method is evaluated on synthetic and real data and compared to other standard unmixing methods to further demonstrate the interest of the proposed strategy.