A Characteristic Function Based Contrast Function for Blind Extraction of Statistically Independent Signals with Symmetric Probability Distributions

Extraction of Statistically Independent Signals with Symmetric Probability Distributions Muhammad Tufail, Masahide Abe, and Masayuki Kawamata Department of Electronic Engineering, Tohoku University 6-6-05, Aza-Aoba, Aramaki, Aoba-Ku, Sendai 980-8579, Japan. Phone: +81-22-795-7095, Fax: +81-22-263-9169 Email:[email protected] Abstract In this paper we propose to employ a characteristic function based non-Gaussianity measure as a one unit contrast function in order to extract statistically independent signals from their linear mixtures. This contrast function is a weighted distance between the characteristic function of a random variable and a Gaussian characteristic function at a finite number of sample points. In case of only one sample point an optimization of such objective function by FastICA algorithm results in a very simple learning rule for the de-mixing matrix. By appropriately choosing the sample point an improved separation performance, especially in a noisy environment, can be achieved.