Design of estimation/deflation approaches to independent component analysis

Adaptive algorithms for independent component analysis (ICA) attempt to extract multiple independent signals from sets of linear mixtures. In this paper, we consider the design of one class of ICA algorithms that combine prewhitening, estimation, and deflation. Both stability and performance analyses of unit-norm-constrained gradient-based extraction methods are derived and used to determine via the calculus of variations the optimum output nonlinearity for the source statistics. Our results show that (i) the local convergence behaviors of these algorithms can be significantly enhanced by matching the output nonlinearity to the source statistics, and (ii) employing a linear term within the output nonlinearity can improve these algorithms' performances. Simulations verify the accuracy of the theoretical results and indicate the performance improvements obtainable by proper algorithm design.