Independent component analysis involving autocorrelated sources with an application to functional magnetic resonance imaging

Seonjoo Lee, Haipeng Shen, Young Truong, Mechelle Lewis, Xuemei Huang

Research output: Contribution to journalArticle

19 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1009-1024
Number of pages16
JournalJournal of the American Statistical Association
Volume106
Issue number495
DOIs
StatePublished - Oct 21 2011

Fingerprint

Functional Magnetic Resonance Imaging
Independent Component Analysis
Spectral Density Function
Marginal Function
Correlation Structure
Density Function
Whittle Likelihood
Moving Average Process
Blind Source Separation
Autoregressive Moving Average
Autoregressive Process
Time Series Models
Marginal Distribution
Likelihood Function
Data-driven
Time series
Independent component analysis
Functional magnetic resonance imaging
Simulation Study
Numerical Results

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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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.",
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Independent component analysis involving autocorrelated sources with an application to functional magnetic resonance imaging. / Lee, Seonjoo; Shen, Haipeng; Truong, Young; Lewis, Mechelle; Huang, Xuemei.

In: Journal of the American Statistical Association, Vol. 106, No. 495, 21.10.2011, p. 1009-1024.

Research output: Contribution to journalArticle

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