Fast and Accurate Methods for Independent Component Analysis

The thesis deals with several problems in blind separation of linear mixture of unknown sources using independent component analysis. Among other things, it focuses on a key question: how accurate the separation can be done, and how to achieve the best possible separation in practice. First, the problem with indeterminacy of order and signs of original sources is addressed. The indeterminacies need to be retrieved in several situations, therefore, a general method for optimum assignment of separated sources to the original or some desired ones is proposed. In order to find out some limit of separation accuracy, Cramér-Rao Lower Bound for linear independent component analysis is derived, which is an algorithm independent bound. It is shown that the bound depends on the distribution of the original sources only. Next, performance analysis of both original versions of a well-known algorithm FastICA is done. It is shown that the bound can be approached is certain scenarios. Based on a simple idea of generalization of a symmetric version of algorithm FastICA, an improved algorithm, called EFICA, is proposed. The novel method is shown to be efficient, i.e. its accuracy attains the CramérRao bound, provided that score functions of the original sources are known. The algorithm is tuned to be efficient for signals with Generalized Gaussian distributions. Computer simulations validate the efficiency and show that the method outperforms other competitive methods in different scenarios. Computational complexity of the algorithm is shown to be reasonably low.