title: Independent Component Analysis Involving Autocorrelated Sources With an Application to Functional Magnetic Resonance Imaging.
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 carried out by relying solely on the estimation of the marginal density functions, either parametrically or nonparametrically. In many applications, correlation structures within each source also play an important role besides the marginal distributions. One important example is functional magnetic resonance imaging (fMRI) analysis where the brain-function-related signals are temporally correlated. In this article, we consider a novel approach to ICA that fully exploits the correlation structures within the source signals. Specifically, we propose to estimate the spectral density functions of the source signals instead of their marginal density functions. This is made possible by virtue of the intrinsic relationship between the (unobserved) sources and the (observed) mixed signals. Our methodology is described and implemented using spectral density functions from frequently used time series models such as autoregressive moving average (ARMA) processes. The time series parameters 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 real fMRI application. The numerical results indicate that our approach outperforms several popular methods including the most widely used fastICA algorithm. This article has supplementary material online.
authors.affiliation: Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599.
authors.forename: Seonjoo
authors.initials: S
authors.lastname: Lee
authors.affiliation: Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599. ( haipeng@email.unc.edu ).
authors.forename: Haipeng
authors.initials: H
authors.lastname: Shen
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 ( truong@bios.unc.edu ).
authors.forename: Young
authors.initials: Y
authors.lastname: Truong
authors.affiliation: Neurology and Pharmacology, Pennsylvania State University College of Medicine, Hershey, PA 17033 ( mlewis5@hmc.psu.edu ).
authors.forename: Mechelle
authors.initials: M
authors.lastname: Lewis
authors.affiliation: Neurology, Pharmacology, Radiology, Neurosurgery, Kinesiology, and Bioengineering, Pennsylvania State University Milton S. Hershey Medical Center, Hershey, PA 17033 ( xuemei@psu.edu ).
authors.forename: Xuemei
authors.initials: X
authors.lastname: Huang
keywords: Blind source separation; Discrete Fourier transform; Spectral analysis; Time series; Whittle likelihood