An Implementation of Ã\x9f-Divergence for Blind Source Separation

Life sustaining biomedical signal processing demands a guarantee that the results produced are accurate and precise. The separation of sources (e.g., demixing two heart signals, one from a mother, and one from a fetus) based only on observations of those mixtures, known as the blind source separation problem, is seen by researchers and scientists as a necessary preprocessing step in order to obtain uncontaminated data for analysis. A method from the field of intelligent signal processing called independent component analysis (ICA) is a promising solution to this problem. However, ICA algorithms and their implementation must be robust to interference, including outliers. Unfortunately, contamination of biomedical recordings by outliers is an unavoidable aspect in signal processing. Mihoko and Eguchi developed an outlier robust ICA algorithm, but code for this algorithm is unavailable. This paper presents a Matlab implementation of their beta-divergence for blind source separation algorithm. The implementation uses a quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization, combined with an Armijo conditioned line-search, to minimize the beta-divergence between the density of the source estimates and the product of its hypothesized marginal densities to separate a mixture of statistically independent sources. The implementation is verified by repeating the source separation simulations published by Mihoko and Eguchi. In each simulation the separation results match visually to those published by Mihoko and Eguchi