TY - JOUR
T1 - Independent component analysis involving autocorrelated sources with an application to functional magnetic resonance imaging
AU - Lee, Seonjoo
AU - Shen, Haipeng
AU - Truong, Young
AU - Lewis, Mechelle
AU - Huang, Xuemei
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80054708838&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80054708838&partnerID=8YFLogxK
U2 - 10.1198/jasa.2011.tm10332
DO - 10.1198/jasa.2011.tm10332
M3 - Article
AN - SCOPUS:80054708838
SN - 0162-1459
VL - 106
SP - 1009
EP - 1024
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 495
ER -