Independent component analysis with optimized pairwise processing

The present contribution investigates the solutions to independent component analysis (ICA) based on the pairwise 4th-order statistics of the observed data vector. Previously proposed solutions to the two-signal scenario, including the well-known JADE, are unified under the general weighted fourth-order estimator (GWFOE). A theoretical asymptotic performance analysis enables the selection of the optimal estimator in the GWFOE class, i.e., the solution with minimum mean square error performance. To extend the pairwise estimators to the general scenario of more than two sources, an improved Jacobi-like optimization (JO) approach with reduced computational complexity is put forward. Adaptive versions of the JO methods are also revised, focusing on the enhancement of their convergence properties. The ultimate goal of this paper is to develop general guidelines for an optimized use of the pairwise processing strategy for ICA.