Joint blind source separation by generalized joint diagonalization of cumulant matrices

In this paper, we show that the joint blind source separation (JBSS) problem can be solved by jointly diagonalizing cumulant matrices of any order higher than one, including the correlation matrices and the fourth-order cumulant matrices. We introduce an efficient iterative generalized joint diagonalization algorithm such that a series of orthogonal procrustes problems are solved. We present simulation results to show that the new algorithms can reliably solve the permutation ambiguity in JBSS and that they offer superior performance compared with existing multiset canonical correlation analysis (MCCA) and independent vector analysis (IVA) approaches. Experiment on real-world data for separation of fetal heartbeat in electrocardiogram (ECG) data demonstrates a new application of JBSS, and the success of the new algorithms for a real-world problem.

► The joint blind source separation (JBSS) problem, which includes canonical correlation analysis (CCA), multiset CCA (MCCA) and independent vector analysis (IVA), is studied.
► A generalized joint diagonalization structure of cumulant matrices is shown and exploited to solve the JBSS problem.
► This generalized joint diagonalization structure is efficiently identified by solving a series of orthogonal procrustes problems.
► Both simulation and experimental results are reported to study the performance of new algorithms.
► The new algorithms can reliably solve the permutation ambiguity in JBSS and offer superior performance compared with existing approaches.