ICA algorithms for 3 sources and 2 sensors

In this paper we develop efficient algorithms to identify the mixing matrix in the context of an independent component analysis with 3 sources and 2 sensors. Our contribution is two-fold. First, by applying twice a theorem by Sylvester, it is shown that the mixture can be obtained analytically by solving a linear system involving cumulants of both orders 3 and 4. Secondly, the latter theorem is extended to the case of “polynomials” of complex variables in which each monomial counts the same number of complex conjugated unknowns; this leads to an algorithm allowing us to identify the mixture by solving a linear system involving only 4th-order cumulants