An algebraic ICA algorithm for 3 sources and 2 sensors

In this paper we develop an algebraic algorithm for Independent Component Analysis with 3 complex-valued sources and 2 sensors. First we consider a generalization of an old theorem by Sylvester, which allows us to relate the problem with the approximation of a 4th-order tensor with Hermitean symmetry by a tensor of rank-1. We present an Alternating Least Squares algorithm for the computation of the result.