Algebraic Solutions to Complex Blind Source Separation

The linear BSS problem can be solved under certain conditions via a joint diagonalization approach of only two matrices. Algebraic solutions, i.e. solutions that only involve eigenvalue decompositions or singular value decompositions, are of particular interest as efficient eigensolvers exist. Success of these methods depends significantly on particular properties of the sources, such as non-stationarity, non-whiteness, nonGaussianity, and non-circularity. In this work, we propose alternative algebraic solutions to solve the complex BSS problem, which generalize the existing approaches. For example, applicability of SUT is limited to the positive definiteness of the covariance matrix, whereas our approach allows to exploit alternative information, such as autocorrelation and pseudo-autocorrelation, to solve the complex BBS problem.