PARAFAC2 and its block term decomposition analog for blind fMRI source unmixing

Tensor-based analysis of brain imaging data, in particular functional Magnetic Resonance Imaging (fMRI), has proved to be quite effective in exploiting their inherently multidimensional nature. It commonly relies on a trilinear model generating the analyzed data. This assumption, however, may prove to be quite strict in practice; for example, due to the natural intra-subject and inter-subject variability of the Haemodynamic Response Function (HRF). This paper investigates the possible gains from the adoption of a less strict trilinear model, such as PARAFAC2, which allows a more flexible representation of the fMRI data in the temporal domain. In this context, and inspired by a recently reported successful application of the Block Term Decomposition (BTD) model to a 4-way tensorization of the fMRI signal, a PARAFAC2-like extension of BTD (called here BTD2) is proposed. Simulation results are presented, that reveal the pros and cons of these tensorial methods, demonstrating BTD2's enhanced robustness to noise.