Nonparametric Independent Component Analysis for Colored Sources with Application to Functional Magnetic Resonance Imaging

• Activity Number: 335
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Young Truong*+ and Seonjoo Lee and Haipeng Shen
• Companies: The University of North Carolina at Chapel Hill and NIH and The University of North Carolina at Chapel Hill
• Keywords: ICA ; blind-source separation ; spectral density ; splines

Abstract

Independent component analysis (ICA) is an effective data-driven method for blind source separation. It has been successfully applied to separate source signals of interest from their mixtures. Most existing ICA procedures are for instantaneous mixtures and carried out by relying solely on the estimation of the marginal density functions. In many practical applications, the sources have temporal autocorrelations, or are mixed with time delays. For the convolutive mixtures, convolutive ICA based on ARMA models have been proposed. In this paper, we consider the case of sources with possibly mixed spectra, where ARMA estimates are often unstable. Specifically, we propose to estimate the spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies and a resting stage EEG data application. The numerical results indicate that our approach outperforms existing ICA methods including the most widely used Infomax algorithm.