Non-parametric Ica

We introduce a novel approach to the blind signal separation (BSS) problem that is capable of jointly estimating the probability density function (pdf) of the source signals and the unmixing matrix. We demonstrate that, using a kernel density estimation based Projection Pursuit (PP) algorithm, it is possible to extract, from instantaneous mixtures, independent sources that are arbitrarily distributed. The proposed algorithm is non-parametric, and unlike conventional Independent Component Analysis (ICA) frameworks, it requires neither the definition of a contrast function, nor the minimization of the high-order cross-cumulants of the reconstructed signals. We derive a new method for solving the resulting constrained optimization problem that is capable of accurately and efficiently estimating the unmixing matrix, and which does not require the selection of any tuning parameters. Our simulations demonstrate that the proposed method can accurately separate sources with arbitrary marginal pdfs with significant performance gain when compared to existing ICA algorithms. In particular, we are successful in separating mixtures of skewed, almost zero-kurtotic signals, which other ICA algorithms fail to separate.