Rank estimation and tensor decomposition using physics-driven constraints for brain source localization

This paper deals with the tensor-based Brain Source Imaging (BSI) problem, say finding the precise location of distributed sources of interest by means of tensor decomposition. This requires to estimate accurately the rank of the considered tensor to be decomposed. Therefore, a two-step approach, named R-CPD-SISSY, is proposed including a rank estimation process and a source localization procedure. The first step consists in using a modified version of a recent method, which estimates both the rank and the loading matrices of a tensor following the canonical polyadic decomposition model. The second step uses a recent physics-driven tensor-based BSI method, named STS-SISSY, in order to localize the brain regions of interest. This second step uses the estimated rank during the first step. The performance of the R-CPD-SISSY algorithm is studied using realistic synthetic interictal epileptic recordings.