1Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the Cramér-Rao Lower Bound

Abstract — FastICA is one of the most popular algorithms for Independent Component Analysis, demixing a set of statis-tically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramér-Rao lower bound. The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian distributions with parameter α, denoted GG(α) for α> 2. We name the algorithm EFICA. Computational complexity of a MatlabTM implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simula-tions corroborate these claims and show superior performance of the algorithm compared with JADE and Non-Parametric ICA on separating sources with distribution GG(α) with arbitrary α, as well as on sources with bi-modal distribution, and a good performance in separating linearly mixed speech signals. Index Terms — Independent component analysis, blind source separation, blind deconvolution, Cramér-Rao lower bound, algorithm FastICA I