Extraction of Correlated Sparse Sources from Signal Mixtures

Abstract

A blind source separation method is described to extract sources from data mixtures where the underlying sources are sparse and correlated. The approach used is to detect and analyze segments of time where one source exists on its own. The method does not assume independence of sources and probability density functions are not assumed for any of the sources. A comparison is made between the proposed method and the Fast-ICA and Clusterwise PCA methods. It is shown that the proposed method works best for cases where the underlying sources are strongly correlated because Fast-ICA assumes zero correlation between sources and Clusterwise PCA can be sensitive to overlap between sources. However, for cases of sources that are sparse and weakly correlated with each other, there is a tendency for Fast-ICA and Clusterwise PCA to have better performances than the proposed method, the reason being that these methods appear to be more robust to changes in input parameters to the algorithms. In addition, because of the deflationary nature of the proposed method, there is a tendency for estimates to be more affected by noise than Fast-ICA when the number of sources increases. The paper concludes with a discussion concerning potential applications for the proposed method.