Basis selection for maximally independent EEG sources

We suggest a solution to the following problem: “Given multichannel linear source mixture data Y, and an overcomplete dictionary, A, of source projections, a_i, how can we construct a complete basis, A₀, by selecting columns from A such that the sources X = A^-₀¹Y are as statistically independent as possible from each other?”. While conventional independent component analysis (ICA) methods learn the mixing matrix A₀ from scratch given Y, we restrict ourselves to selecting basis vectors from a known overcomplete dictionary. We develop two methods based on modifications of the maximum likelihood equivalent of the Infomax approach and the reconstruction-ICA (RICA) algorithm. We show that on realistic synthetic electroencephalographic (EEG) data our algorithms can find the true sources in the case of a highly coherent dictionary while requiring relatively fewer data points compared to other algorithms. On real EEG data, our algorithms obtain higher mutual information reduction.